Colosso is a tournament held in Tolbi every year. At Babi's suggestion, Isaac enters this competition.
Before entering Colosso, give Isaac all the Psynergy-granting equipments. These will give you a great advantage when it comes to race time. Head directly to the Colosseum as soon as you reach Tolbi. Walk around the stairs and up until the guards recognize you. They'll take you to the waiting area. After a short cutscene, you will be taken to the stage where the Colosso tournament's first round occurs. Listen to the guard's explanations, as they are quite helpful. When he finishes you'll be able to pick where you want each member of your party to cheer you on from. By using Psynergy, some of your party members will be able to affect the layout of the stage in your favor; choose carefully where you want to do this from.
Note that if you lose the Colosso tournament, it will not result in a game over, nor is there any real negative repercussions. Do try to win however, as there are some nice bonuses from doing so.
Colosso: Round 1
For the first stage of Round 1, you have to push a stump down to jump across. Leave Garet to cheer for you here, as he can use Move to help you get across faster. For the second stage, there is a water basin which acts as a scale. Leave a character with Douse here, and they can fill the basin to save you some time. Ivan is a good choice, so equip him with the Douse Drop and leave him here. In the third stage, there is a small plant. Give Mia one Venus Djinni so that she will learn Growth, then leave her here. The fourth stage has no way for a party member to help you, so ignore it. Now that all your party members are in a stage, go to the guard again and return to the waiting area. Save, then go stand in the circle at the far right. The guard will ask if you're sure, then say yes.
Now, it will give you an opportunity to control the other party members. Move the stump in the first stage to the left one, use Douse on the basin in the second stage, and use Growth on the plant in the third stage. It is finally time to race: run along the path you have created as fast as possible, but don't pass up those treasure chests. Make sure you reach the end quickly, as the Iron Shield is significantly better than the leather gloves.
Then, you must battle Azart. Ragnarok is an amazing skill for this first fight. Granite will cut down on the damage you take rather significantly, so use it first off. Flint and Sap are also very useful. Use the Nut if you need it, and then summon. If you get low on HP (after every 2 attacks or so) use Cure Well also. It shouldn't take too long, and once you win, you'll be returned to the waiting room.
Colosso: Round 2
The first stage of round 2 has several stumps against the wall. Leave Garet here so that he can Move them. For the second stage, you could leave someone with Halt, preferably Ivan, to stop the man from turning the lever. The third stage has two small puddles which can be frozen with Frost. Leave Mia here. The fourth stage, again, has no way that you can be assisted, so don't leave anyone here; however, you can see that there is a vine on the other side of the fence, so give Isaac a Mars Djinni so he will be able to use Growth later on. In the fifth stage, there is a log which has a crack in it. It can be knocked over with Force, so you could leave a person with that ability here, perhaps as an alternate to leaving Ivan at the second stage. Save, and again, return to the guard and he'll take you to the waiting room once more.
When you are able to control the other party members, have Garet Move the middle log to the left. Take Ivan and either have him Halt the person working the lever. Or, if he's in the fifth stage, move him over to the right side of the log, and hit it with Force so that it falls in the water. Have Mia Frost the left puddle. Run as fast as possible once the contest starts to get as much of the treasure as possible. There are two nuts and a Smoke bomb here. Get to the end, and hopefully grab the armor instead of the Cotton Shirt.
Now, you must fight Satrage. Hit him with your Mars Djinni first to get your regular Psynergy attacks back. As before, Ragnarok is a great skill, and so are the Djinn and summons. Satrage is mostly concerned with inflicting status effects, so beware of those. His hits do a bit more damage than Azart's, so you will need to heal more often. Sap comes in especially handy in these scenarios, as it allows you to recover HP and deal damage at the same time. After a short while, you'll defeat him.
Colosso: Round 3
The first stage has a water puddle underneath a platform. You will want to leave Mia here. Stage 2 has a stump that you can Move, so Garet will cheer from here. The third stage has a man operating levers, you can use Halt on him; but it won't be as helpful, so ignore it. In the fourth stage, you can see that there is a small plant to grow, but it can't be reached from the crowd. Give Isaac a Mars Djinni (or leave the one from round 2 with him.) The fifth stage has a log which needs Force on it once again, so leave Ivan here with the Force Orb. There is a sixth stage, but you have no more party members, so return to the guard.
Once you are controlling your party members, have Garet Move the pillar to the right, have Ivan use Force on the log to stop the conveyor belt, and then have Mia Frost the puddle to raise the platform. Then begin racing. When you come up to the small plant, use Growth on it to save a lot of time. Try to grab the better sword, or you'll be left with a Hunter's Sword.
This match is against Navampa; use your Mars Djinn first to return your class to normal, then start using Venus Djinni. After you have used three of those, summon on him. Heal as necessary, as Navampa is significantly stronger than the other two, especially if you don't get the best sword. Use Djinn and Summons exclusively to attack, as you need your PP to heal. Once he is defeated, you both will collapse. The party rushes up to you and drags you away.
After a cutscene, you will be lying in bed. Press left to get out. The cutscene will continue, then you will be free to walk. All your equipment has been returned, so give the items back to their proper owners. Walk out of the room and up the stairs to Babi's throne room. If you won, he will give you the prize for victory, the Lure Cap. A long cutscene will begin, describing Babi's goals and talking about Lemuria. Babi is running out of his Mystic Draught, which is extending his life. He has taken three separate measures to find a solution: First, establishing the Colosso tournament to search for warriors capable of using Psynergy; Second, funding the research of Alchemy by many scholars, like Kraden; and finally, the construction of the Babi Lighthouse near Lalivero to help his ships find Lemuria again. Iodem will be accompanying you, and everyone agrees to meet at the Gondowan Passage to the south. Babi goes down to his bedroom. Follow him, and you will see a black sphere sitting on the nightstand. If you attempt to pick it up, Babi will ask if you want it. Tell him yes, and you will be allowed to take the Cloak Ball, which grants the Cloak Psynergy. This is necessary to clear the optional Lunpa sidequests.
You can now finish up any business that you have left, and head to Gondowan Passage.