You should know this for your sanity, but it is not essential. Nineveh has 25 warships, and they will attack you. After that, Nineveh is static. They have no Transports, and will not be able to build any until way too late, if at all, so they can never invade you. Furthermore, you won't need to fight your way through all of Nineveh's army, because they need to defend all routes to the Wonder, and you only need to use one of the routes.
As a general rule, an AI will be reluctant to attack you if it thinks you are too strong, so you should keep your fleet strong.
Nevertheless, this is an expert scenario. If you really know what you're doing, you will find the scenario challenging, but well within your capabilities. If you don't really know what you're doing, you will have great difficulties.
Babylonians have a specific tech tree, and in particular, they don't get Triremes or Catapult Triremes, but they do get second-level catapults, as well as the catapult range upgrade. You will have noticed by now that there were significant variations to the tech tree in this campaign, and this is true in this scenario as well. You are actually using the Egyptian tech tree here. You will be able to produce both Triremes and Catapult Triremes, which is quite important here. Therefore there is no real point in trying to convert Nineveh's ships. On the other hand, you will not get second-level catapults, although you still get the range upgrade.
Your most important units are priests, catapults, and warships. Therefore, you will be producing as many of them as you can afford. A strong navy is extremely important on a water map, and can generally actually win the scenario almost entirely by itself. Here you will aim to maintain a fleet of 10-15 warships in good condition. Because Nineveh doesn't have any production, you might be able to get away with the smaller number. You will want to have 4 catapults and 4 priests for sure, and maybe a few more priests. You will want 10-15 villagers, aiming for the smaller number unless that turns out to be too low. This puts you at about 35 population. You will want 5 archers, 5 cavalry, and 5 good melee troops, and suddenly you are at the population limit. Accordingly, think carefully about the population limit when producing units, and only produce what you actually need.
Let's look at our initial wood stockpile (2500). You need 200 (Town Centre) + 720 (4 catapults) + 75 (War Galley research) + 150 (missile weapon range upgrade) + 175 (building size upgrade) + 1080 (8 warships) = 2400, leaving you with 100. Make sure that you don't deviate from this list until you have at least a minimal wood income.
Let's look at our initial gold stockpile (2000). You need 500 (4 priests) + 320 (4 catapults) + 800 (Iron Age research) + 350 (to convert enemy buildings) = 1970, leaving 30. If you deviate from this list, you will regret it. You will be able to bring gold in before too long, but you definitely will not appreciate having to wait to be able to convert enemy buildings.
Let's look at our initial food stockpile (2000). You need 150 (War Galley research) + 170 (missile weapon range upgrade) + 150 (building size upgrade) + 400 (8 villagers) + 100 (one Scout) = 970. This leaves 1030, which looks like a lot, but save it all to research Iron Age. You can produce a couple of fishing boats to bring in a bit more food, or you might be able to take some from Yellow, but it's not that important. You won't actually be needing any more ground troops than those already listed, because Nineveh can't invade you, and Yellow won't get through your fleet.
Food is not a concern for a long time. Stone is also unimportant for now.
Nineveh starts building a Wonder either right away or very soon. Because they only have one villager building it, it takes about one minute of game time to complete 1% of it, which means that you have about 100 minutes of game time minutes to kill that villager, and some more time after that to blow up the Wonder if you didn't kill the villager in time. Keep an eye on the Wonder if you have a breathing space, but you really should ignore it for now and concentrate on more immediate concerns.
First, research War Galley. Second, jump via the mini-map to the proper location to do the next four operations without needing to move the map window. Third, produce a priest. Fourth, produce a catapult. Then research the missile weapon range upgrade and the building size upgrade. Jump back to your fleet, assign it a control number, explore the immediate vicinity, and "hide" your ships along the map edge. Pause the game, think about what you have done so far, and think about what you need to do next.
The mini-map should not show any hostile presence at this time. Nothing will happen before War Galleys are available. A little bit later, your first priest will arrive, and a bit later, your first catapult will arrive. You will be landing on the landmass to the west as soon as you have even one unit available, which, as it turns out, will be a priest. You have space for 27 new units. Keep track of your population.
Unpause the game, select your dock, and just wait until you can start producing War Galleys. Then select your temple, wait until you can produce your second priest, and send the first one into a Transport. Send your first catapult up to support your northern Tower and start your second one.
At about this time, a squadron from Nineveh will attack towards your dock, picking on your ships if they can, and your northern Tower may be attacked as well. Regardless of what you were doing at the time, as soon as you see red dots on the mini-map, jump over there and assume tactical control. Sink the Catapult Triremes first with mass fire from your fleet, avoiding their rocks, of course, and then keep mass firing on one target at a time. If you can, move whichever ship of yours that is taking the most fire sideways. After this fight, use your catapult to sink or distract any enemy ships that are attacking your Tower. When the smoke clears, pause the game and rest.
Your production plan is probably in disarray right now. Get it moving again. The configuration you are aiming for is that your first two catapults and second and fourth priests support your northern Tower, while your two other priests and catapults start working over Yellow. Get all new production ships to the front, and keep them coming until you reach the target number. Send all badly damaged ships to the rear. This isn't critical, because you have and will have plenty of wood, and maybe you don't want to spend time and effort on preserving and repairing your ships, but the AoE expert accumulates small advantages whenever possible, and repairing ships is a lot cheaper than building new ones. Furthermore, the AI probably treats your badly damaged ships hiding in the back as though they were new when deciding whether to attack you. If Nineveh is afraid to attack you for a while, then you can really lean hard on Yellow, and you actually have a very good chance of wiping Yellow out real soon.
Get your first priest onto the western landmass ASAP. He should detect at least one Yellow Tower, but more importantly, there is a Grey villager trapped along the map edge. Convert him, stat! He will most likely not be able to escape. Bear in mind that you are using Egyptian stats, and your priests have +3 range. If he does manage to escape somehow, you should consider restarting the game, but it probably isn't critical. In any case, you will shortly have two catapults, two priests, maybe some converted units, and a whole bunch of War Galleys pounding on Yellow, and frankly, you should be able to kill them entirely before too long. Just make sure that you get at least one villager out of all this! If your first villager came from Yellow, get him over to your base right away and get your economy rolling. However, this walkthrough assumes that your first villager came from Grey. If you successfully converted him, this would be a good time to save the game.
Your first villager should build a Town Centre right away, as far towards the coast as possible. Then start pumping out villagers and collecting wood. It is important to get at least one villager out of the trap very soon, and the fastest way available is Grab-and-Dump Forestry. However, this requires a lot of micromanagement, and you need a lot of wood anyway, and villagers cut through forests pretty fast in AoE, so it is probably best to just keep the woodcutting oriented towards the east and put your main attention elsewhere.
Grey actually has a second villager waiting for you to convert him. Technically, you need to be careful about building a Town Centre next to him if he's still alive, because if he decides to attack it while it only has one hit point, you've just lost 200 wood that you can't afford at this point. However, because Grey doesn't actually have a base, their second villager probably won't be getting all territorial on you.
Even though Yellow is actually significantly superior to you in total at this point, you have an effective strong superiority because you are defining the terms of the conflict. You have catapults to blow up their Towers and priests to heal your damage and to take over the most powerful enemy units. If the Yellow army becomes at all threatening, you can leap back into your Transports, at which point the attacking enemy units tend to become catatonic, and your fleet will waste them very easily. In any case, your 5-10 War Galleys will be able to eradicate all the Yellow troops that come out to play easily, although they need to stay away from the Towers. Yellow doesn't really have a chance. If their troops stay in their base, you can blow up their Towers with impunity. If they come out of their base, your fleet will kill them. Furthermore, Yellow will try to invade you, but your fleet controls the invasion route. You can sink all of their Transports without difficulty, either loaded or empty. It won't be long before the Yellow dock is gone, and their army is dead, and all their villagers, who rushed out to repair their buildings, are also dead.
Yellow's best option is actually to stay in their base and keep their economy going. That way, you will need to go in and get them, and you won't have your fleet to help. If you do start running into Yellow priests, your best bet is probably to pull back, get Monotheism, and attack the Yellow priests with your own.
When you know from the Achievements that Yellow has no more units, produce a Scout and explore the western landmass. You find an enormous amount of resources of all types. There are a few Towers that you need to destroy, but your two catapults will make short work of them. If you haven't already done so, research Iron Age. Then research Monotheism and start converting the Yellow depot buildings.
By this time, you have probably collected way more wood than you will need in this scenario. Switch to food and gold, and maybe a bit of stone. You probably won't do much farming in this scenario, because there are so many better food sources available. Don't hunt Gazelle; it's just too much bother. Elephants are OK, as long as you don't get distracted and lose a hunter.
Repair all your damaged ships, and upgrade to Trireme. Prepare to produce some Catapult Triremes. When you have a dozen Triremes in good shape, sweep Nineveh's ships off the face of the Earth. As long as the Wonder is no more than half built, you are on schedule.
As you push forward, you start to engage Nineveh's coastal defenses. Towers are not a problem, because some or all of your warships outrange them. Siege weapons can always be outmaneuvered by warships. Archers, even elephant archers, will be crushed by the massive firepower of your fleet. You will need to repair your ships from time to time, but that's OK. Priests are always a problem. They will get lucky, or they won't, but you can't control it. However, don't expose your Catapult Triremes, and hit the priests with extreme prejudice and as much instantaneous firepower as you can muster. Nineveh is flanked by two islands that have some Towers on them, but no enemy units. Your fleet, supported by your catapults, can clear these islands without difficulty. This will give you repair bases close to the action, as well as a lot more resources.
It is easier to invade Nineveh from the east because you have more maneuver room for your ships over there. You will probably not be able to blow up Nineveh's western docks under the circumstances. You need to be aware of the possibility that they could produce more ships if you knock them down below 50 population.
When you have cleared as much of Nineveh's eastern coast as you can with your fleet, it's time to start landing troops. You won't actually need anything more than your 4 early catapults and 4 early priests and a couple of villagers, upgraded as much as possible, of course. Your initial landing forces will probably need to retreat to their Transports a couple of times, while luring the counter-attacking enemy units into range of your fleet.
If you have any spots open in your population roster, which you should have, because you had no real need for ground troops yet, fill them with catapults and priests, and maybe a couple of chariot archers. Disband unnecessary and ineffective units if necessary.
The best landing spot is right on the eastern map edge. This is because the map edge protects your flank. After wiping out about two waves of defending troops, and blowing up four Towers inland, the road to the Wonder is completely open. You should then be able to walk a priest right up to the Wonder with impunity. At this point, assuming the Wonder is not finished yet, you could win the scenario simply by converting Nineveh's only villager. That might cost you a priest, but it would be worth it. Technically, you don't win until the Wonder is destroyed, but once the time pressure is off, you will be able to end the scenario any way you like. On the other hand, depending on how much time you have left, you could advance against the Wonder more deliberately, or you could do a suicide strike against the villager with cavalry.
You may decide to also advance towards the Wonder along the central route. Aside from Nineveh's regular troops, there are also 4 trapped Orange Catapults blocking this route. The only units you have that outrange them are your priests. Accordingly, the easiest way to eliminate these units is to convert them, which is equivalent to killing them.