Here is the full list of all 24 The Light Brigade achievements.
Have a hypnotized enemy kill another enemy.
Cock an ally Light Brigade soldier's rifle.
Land 250 headshots. (accumulated)
Hold onto 1,000 coins at once during a run.
Finish your first run, start to finish.
Spend 1,000 gold at a store.
Defeat the Father.
Land 250 gunshots. (accumulated)
Travel 1,000 meters. (accumulated)
Reload 100 times. (accumulated)
Try to fire your weapon without first reloading it.
Use an enemy's dropped weapon to kill another enemy.
After death, find your ghost and pray to it.
Kill an enemy bomber using a grenade.
Pray to the Mother.
Die and be revived for the first time.
Defeat the first boss.
Defeat the second 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.
Use the wishing well.
Kill an enemy sniper from far away.
Kill an enemy priest using magic.