General Strats for Co-op Campaign

Old Town
Not much in terms of strategy here. Just move through the objectives in the intended way, and don't worry about the secondary objective until the end. You can fail or complete the secondary objective to help the pinned down troops and the level will still finish. 

Wharf
All the crates you have to blow up can be hit from the right side of the wharf using a grenade launcher. Look at either my solo co-op campaign run, or my duo co-op campaign run with NateDawgg to see the place in the clouds you need to line up with to get the hit on the crates. The place you need to aim changes depending on if you are doing full screen or split screen.
Do not complete the secondary objective to collect intel as it's not necessary and completing this objective can cause a glitch where the helicopter won't pick you up and you can't finish the level.

Treasury
The anti-air things you have to destroy can all be destroyed using the turrets on top of the central bridge in this level. See my run to see where to aim the turret to destroy them. Other than that, this level is pretty straightforward.

Temple
This level has some RNG as to where the enemy leader is located so you might want to do this level first. If the enemy leader is located on the lower level in the back of the temple, you can fire a grenade at the right spot and kill him instantly without having to battle all the other guys in the temple. Again, see my run to see an example of this.
When completing this level, when you get to the evac zone, all the enemies on the map will converge on your location and you have to fend them off; however, after hitting the evac zone and triggering the helicopter to come, you can immediately run away from the evac zone. All the enemies will still go to the evac zone and you can shoot them from a distance instead of having to fend them off, making it a lot easier. See my solo co-op campaign run for an example of this.