This is actually easier than the previous mission. The attacks on your base don't start so early, and while you have a big fight in the end, you'll have way more space to maneuver instead of attacking a funnel kill zone.
The map is divided by a river and the only bridge is closed, so the mission as two distinct parts. First of all, turtle. Take the 2 Strategic Points right in your base and don't go out. This way you can build and tech up for quite a while. Make several generators, tech toward vehicles as soon as you can. You also need 1 missile squad in case you get tank-rushed before that, and some anti-infantry (like 1 flamer squad and 1 heavy bolter squad). Build turrets.
You will eventually be attacked from all directions except below, but the big ones (with vehicles) come from the left. Only 1-2 infantry squads at a time from the other entrances. When you can spare the troops (say 1 Dread & 1 squad), go get the SP on your right. Also get the Relic, it's unclaimed. These will be left almost completely alone. When you get the left SP it will draw tank attacks and the like so don't go there until you can handle it.
When you have 2 lascannon Predators, you should take out the left side (minor Eldar base, Slag Deposit, Relic) without trying. Then send Skull Probes to scout the main base. Note that you can attack it from behind if you want, right where the production buildings are. They don't have decent anti-vehicle so Preds and Dreads will own them. Then clean your side of the river (lone squads will keep appearing at certain locations throughout the mission, you can't stop those). Before taking the gate-opening Strategic Point, stop.