Here is the full list of all 38 Space Gladiators trophies - there are 24 bronze, 8 silver, 5 gold and 1 platinum.
Die for the first time.
Unlock all trophies.
Kill 100 enemies.
Kill 250 enemies.
Kill 500 enemies.
Kill 1000 enemies.
Destroy 100 destructibles.
Destroy 250 destructibles.
Destroy 500 destructibles.
Destroy 1000 destructibles.
Destroy 100 destructibles in one run.
Buy 50 items.
Kill 5 enemies with deflected trap bullets in one run.
Pick up 4 items from a demonic altar without dying.
Hold 500 coins.
Buy 20 items in one run.
Escape Tartarus without using any abilities.
Escape Tartarus without picking up items. (starting gear and arena rewards allowed)
Get all characters to level 5.
Defeat any boss as Robbie with an Alien Arm.
Defeat Lost Soul without taking damage.
Defeat The Engineer without damaging him with a normal hit.
Escape The Hole.
Escape The Colosseum.
Escape the Untamed Jungle.
Escape Tartarus.
Escape The Hole in under 6 minutes.
Escape The Colosseum in under 13 minutes.
Escape the Untamed Jungle in under 21 minutes.
Escape Tartarus in under 25 minutes.
Defeat The Abomination.
Defeat the Ogre Champion.
Defeat the Athletic Insects.
Escape Tartarus in Danger I difficulty.
Escape Tartarus in Danger II difficulty.
Escape Tartarus in Danger III difficulty.
Escape Tartarus in Danger IV difficulty.
Escape Tartarus in Danger V difficulty.