Can be done on one console or over Xbox Live. Play these separate 50 levels(not the same as the the 50 single player)
Some advice, when people cannot communicate, use your LT to countdown from 3.
Use 'Splode Tossing and Dual 'Splosions often. Dual 'Splosions are an excellent way to reach places not normally reachable by your three 'splosions.
The Three bosses are the same as before. You essentially only pay attention to Player 1 (Red 'Splosion Man) so while the boss is distracted by P1, be sure to attack when you can. such as if one of you should fall, try to deflect what you can.
Try to avoid using the "Way of The Coward" option, because you have to go back and complete that level for the achievement... Just like the achievement "You're The Best Around" you must have all the levels complete, not just the bosses.
There are also 47 Cakes like in single player.... But that's another achievement...
Good luck and Have Fun!
Edit (8/1/09): I have been getting comments on "It always lags for me" or "The people i get lag themselves to death..." the problem there is your connection. If you are experiencing lag while playing with one of your friends, have your friends check their connection and you check yours. 'Splosion Man is a very picky game. I have had these same problems. You need a great connection with your friend/person/people you are playing with. timin is a must which is why a good connection is also a must
Second Edit (8/7/09): It has been brought to my attention that I was not clear on how you have to finish the levels. All 50 levels must be complete, from level 1-1 to level 3-18. You must complete all the levels, even if you join someone in progress the levels will not show available for Time Trials until you have finished the levels before it.
Third Edit: (9/2/09): Thanks to a very abrasive yet informative comment about connections. When experiencing lag and other connection problems I said to "Fix your connection". What i was trying to get at is that you are probably having connection issues when one of the players isn't directly connected to a modem and playing through a router/wireless adapter. I have these same problems because I am hooked up to a router. The router you have acquired should have came with a User Manual. Follow the instructions in the User manual on how to set ports for your Console. I apologize for the lack of detail on how to do it but there are many different routers and i don't know how all of them work.
Fourth Edit (11/12/09) Thanks to Decokiller I an glad to inform you the connection issues have been rectified. Still you may have connection problems though, but that's just because of your general connection with the person. As I have been told it is best to do this in local multiplayer.