Here is the full list of all 29 Rick Henderson trophies - there are 12 bronze, 10 silver, 6 gold and 1 platinum.
Unlock all other trophies.
Attain private rank.
Attain corporal rank.
Attain sergeant rank.
Attain lieutenant rank.
Attain captain rank.
Attain major rank.
Attain colonel rank.
Collect 100 ranks.
Finish a loop.
Enter asteroid field 3 times.
Enter laser barrage 3 times.
Enter meteor storm 3 times.
Enter minefield 3 times.
Kill 100 enemies.
Kill 250 enemies.
Kill 500 enemies.
Kill 750 enemies.
Kill 1000 enemies.
Kill 2500 enemies.
Kill 3 bosses.
Kill 6 bosses.
Kill 12 bosses.
Kill 100 transports.
Collect 25 gems.
Collect 50 gems.
Collect 75 gems.
Collect 100 gems.
Collect 150 gems.