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