Here is the full list of all 15 Billy 101 achievements.
See Billy for the first time
Destroy the enemy gunslinger
Destroy the kamikaze enemy
Get an upgrade
Die in the fire
Use the weapon for the first time
Use robotic arms for the first time
Use the rocket boot for the first time
Use the air booster for the first time
Use an access card
Go through a laser
Destroy an enemy with bazooka
Face the final boss
Beat the final boss
Complete all achievements