Here is the full list of all 24 The Light Brigade achievements.
Land 250 headshots. (accumulated)
Try to fire your weapon without first reloading it.
Have a hypnotized enemy kill another enemy.
Use the wishing well.
Kill an enemy sniper from far away.
Cock an ally Light Brigade soldier's rifle.
Reload 100 times. (accumulated)
Land 250 gunshots. (accumulated)
Use an enemy's dropped weapon to kill another enemy.
Spend 1,000 gold at a store.
Defeat the first boss.
Defeat the second boss.
Rescue an ally Light Brigade soldier out on a run.
Travel 1,000 meters. (accumulated)
Hold onto 1,000 coins at once during a run.
After death, find your ghost and pray to it.
Pray to the Mother.
Die and be revived for the first time.
Finish your first run, start to finish.
Never miss a shot during a fully completed run.
Every single shot during a fully completed run is a headshot.
Kill an enemy bomber using a grenade.
Kill an enemy priest using magic.
Defeat the Father.