Here is the full list of all 19 Project Starship trophies - there are 10 silver, 8 gold and 1 platinum.
Unlock all other trophies
Collect 50 pickups
Kill 4 bosses
Encounter 6 mad events
Kill 300 enemies
Collect 25 pickups
Encounter 3 mad events
Lose 24 shields
Beat highscore of 10,000
Beat highscore of 50,000
Beat highscore of 100,000
Lose 16 shields
Kill 2 bosses
Encounter 1 mad event
Kill 100 enemies
Kill 1 boss
Collect 5 pickups
Kill 25 enemies
Lose 8 shields