Here is the full list of all 21 Helvetii achievements.
Beat level 1
Beat level 2
Beat level 3
Beat level 4
Beat the Matrons
Have more than 100 coins on you during a run
Get a 200+ combo
Obtain an S rank
Obtain an S rank against Octavius
Beat normal mode
Beat hard mode
Beat frenzy mode
Beat every type of challenge room
Bounce off an enemy's head 5 times with disrespect
Fully upgrade the same god to level 3
Get a triplet at dice
Buy a costume
Obtain 50% of all upgrades
Obtain every single upgrade
Obtain every achievement
Taunt after doing a 100 combo