Here is the full list of all 39 No Heroes Allowed! trophies - there are 14 bronze, 22 silver, 2 gold and 1 platinum.
Unlock all trophies in No Heroes Allowed!.
Complete Area 1: Dundadundunduuun Tower.
Complete Area 2: Ludgala Tower.
Complete Area 3: Castle Noneim.
Complete a Daily Challenge.
Unlock Difficulty Level 5 in Daily Challenge.
Attempt the God Aptitude Test for the first time.
Pass 30 stages of the God Aptitude Test.
Complete a Training Stage.
Complete 10 Training Stages.
Complete an Advanced Training Stage.
Score an A or better in 15 or more Training Missions.
Play any area in Story Mode on the l33t difficulty.
Obtain the Waterstarter Pickaxe.
Obtain the Pathfinder 6000 Pickaxe.
Obtain the Snoozerator Pickaxe.
Protect two allies from heroic capture in any round of Story Mode.
Create a Spirit.
Create an Omnom.
Create a Lilith.
Create a Dragon.
Create a Lizardman.
Create an Aquachnid.
Create a Thunderhead.
Create a Hurtle.
Create a Lorelei.
Browse the Almanac for the first time.
Complete 50% of the Almanac.
Activate any type of rune.
Summon a Mara.
Achieve a high dungeon intelligence.
Invited heroes into the dungeon early.
Culled your minions.
Defeat pwner666 in Advanced Training 16: Battle Stations!
Activate the power of any pickaxe.
Create a Slime.
Create 20 Slimes.
Create 50 Slimes.
Create 100 Slimes.