Here is the full list of all 13 Euclidean achievements.
Die 5 times
Die
Dodge a roving creature by Phasing
Die on a stage floor
Get killed by a roving creature while still recharging Phase
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