Here is the full list of all 12 Awesomenauts trophies - there are 7 bronze, 4 silver and 1 gold.
Win an online game session.
Reach max level.
Collect 35 Solar on a drop-pod drop.
Kill the Solar boss in an online game session.
Unlock 3 characters.
Get a killing spree.
Make the most kills of both teams in an online game session.
Win a game session with 2 friends splitscreen.
Play a game session with friends invited through the game session setup.
Win game sessions with six different characters.
Destroy 25 turrets.
Kill 1000 droids/creeps.