Here is the full list of all 21 Awesomenauts Assemble! trophies - there are 21 bronze.
Play against a team with the same Awesomenauts.
Kill 1000 droids/creeps.
Collect 35 Solar on a drop-pod drop.
Destroy 25 turrets.
Win game sessions with 8 different characters.
Earn a total of 10000 Solar ingame (late game bonus does not count).
Win a game in less than 10 minutes.
Kill 25 enemy Awesomenauts.
Taunt an enemy after killing him.
Taunt an enemy after he killed you.
Get killed by a creep.
Get first blood.
Win an online game session.
Make the most kills of both teams in an online game session.
Have more than 500 Solar at once (late game bonus does not count).
Kill 3 enemy Awesomenauts without dying.
Kill an enemy Awesomenaut without buying any items.
Unlock 3 characters.
Win a game session with 2 friends splitscreen.
Play a game session with friends invited through the game session setup.
Reach max level.