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