Shank

The co-op is pretty straightforward but the bosses are what makes this a real cooperative effort.

1st boss: Denny and Dusty--These two are difficult only because they're together for the majority of the fight but after a while they jump to either side of the screen. The trick is for you and your partner to stay in the middle and hit RB over their heads. They crash and once they're knocked out, attack both with RT. Notice that Denny loses more health so when your fighting, go for him first.

2nd boss: Masked Butcher--The walls will not save you at all...in fact you're putting yourself in danger by climbing the walls. Trust me. Basically, aside from putting damage on him with your weapons, he will go to either side of the screen and throw barrels at you. You can shoot them or throw a grenade. Once he's stunned, steer him into the wall.

3rd boss: SWAT boss--This fight is probably the hardest one. Not only does this guy have a grenade launcher and a stun gun, he has 3 backup guys with him. When he engages you with the stun gun, make sure you hit LT and counter him. This will knock you out but your partner can go over to him and hit RT. The backup guys might interrupt but rinse and repeat the counters.

4th boss: Bodyguard--This is simple enough but hard to do when you're getting kicked against the wall. Climb the walls and jump over him. He'll jump high and land with his foot in the ground. Jump him and go back to the walls. If he grabs your partner, grenade or shotgun will release him.

Side note--If your partner is down but surrounded by an enemy, let him sit for a while, go for the enemy and then pick him up. Saves time and keeps you alive longer

The local only co-op is the backstory to Shank's Single Player game and is comprised of several levels with 4 major boss fights, which are rather challenging. Grab a couch buddy and dive straight in, having someone who has played the game before helps as well as there are no tutorials in the MP.
'*NOTE: I personally completed the SP on normal difficulty first, so I'm not sure if the SP opens up all the weapons in the MP, if anyone can confirm this in the comments it would be great.

As this is a game more of skill than strategy, for anyone who is having trouble see below a video walkthrough I found on Youtube. All credits go to the author 'MaholoVideoGames' as they are not my own (I wish!).