Here is the full list of all 13 Euclidean achievements.
Get killed by every creature type in the game
Die 25 times in the same stage
Die 50 times
Win the game
Avoid every creature type by phasing
Die 10 times
Die on a stage floor
Dodge a roving creature by Phasing
Die 5 times
Get killed by a roving creature while still recharging Phase
Die
Get killed by a gargantuan creature in permadeath mode
Win the game with permadeath enabled