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