Here is the full list of all 24 The Light Brigade achievements.
Use the wishing well.
Defeat the first boss.
Rescue an ally Light Brigade soldier out on a run.
Land 250 gunshots. (accumulated)
Land 250 headshots. (accumulated)
Reload 100 times. (accumulated)
Hold onto 1,000 coins at once during a run.
Try to fire your weapon without first reloading it.
Spend 1,000 gold at a store.
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.
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 sniper from far away.
Kill an enemy bomber using a grenade.
Kill an enemy priest using magic.
Defeat the second boss.
Defeat the Father.
Have a hypnotized enemy kill another enemy.
Cock an ally Light Brigade soldier's rifle.