Here is the full list of all 22 PUTRID SHOT ULTRA achievements.
Defeat Big Head and the Unshackled Minds
Defeat the Queen and her infestation
Defeat the Putrid Knight
Defeat the Putrid Knight with Telekinetic Greatsword equipped
Reach Zone 3 with Rapid Arrows equipped
Reach Zone 3 with Rapier Pierce equipped
Reach Zone 3 with Crescent Banana equipped
Yar har! Have 15 or more swarthy oars orbiting ye!
Have 15 or more clean spritz clouds on the field at once
Perform 12 katana X slashes in a row
Spend 15 upgrade points at the upgrade bench
Deal 16 damage with a single bullet
Reach a clip size of 12
Reach 18 max health
Have 20 or more orbital frosts around you at once
Deal over 80 damage with a single attack
Upgrade your ice damage 4 times in a single run
Upgrade your fire damage 4 times in a single run
Upgrade your metal damage 2 times in a single run
Beat an elite with only 1 health remaining
Pick up 100 sandals in a single run
Complete a run with a challenge level of 3 or higher