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