Here is the full list of all 14 Big Sky Infinity trophies - there are 11 bronze, 2 silver and 1 gold.
Classic Mode - Defeat all bosses in one round!
Get a highscore of 125,000 on each mode
Destroy 20,000 enemies
Buy the shop!
Peacefully survive a Black Hole!
This ship is fast and powerful
Get a x100 multiplier!
Smash through difficulty level 7
Destroy 5 enemies at once using a Boomer
Get a highscore of 50,000 on each mode
Spend 20 seconds in the heart of an asteroid
See everything
Destroy 1,000 bad guys
Make a nearby bad guy envious of your drill