I feel you spent most of the time working on this to get the multiplayer running, which is cool, but the mechanics could use more polish. Namely you can't jump half the time. You probably fixed it in the 0.1 version, but I tested the original zip version posted. Sorry.

Pretty good start. I like the idea of competing for destroying monsters, (I assume, I couldn't play Multiplayer). I think it needs a lot more polish, though. I would occasionally get stuck and I'd have to re-click my movement buttons. I could see past the background to the blank color at the edges of the screen as well. I think some audio cues and animation would help with the aesthetics, and probably cut off the exterior edges with a dark black or an earth tone to blend in with the tiles so it doesn't feel like you're in this floating square. There doesn't appear to be any Win/Lose conditions as far as I can tell, and make sure you put in an exit button so we don't have to Alt+F4. Nice start; I think this could be pretty cool with some more work!

All in all, good job!