Here is the full list of all 21 Mount & Blade: With Fire and Sword achievements.
Using any firearm; kill 100 enemies.
Tend to your army's illnesses, five times, by resting or feeding them.
Start any main storyline quest found in the three main factions.
Build a wagon fort from the camp menu.
Customise your mercenaries' equipment using the mercenary camp.
Get in a bar fight.
Buy drinks for everyone at a bar.
Earn 3,000 thaler in profit from a single caravan trade.
You've made 100,000 thaler from using trade caravans.
You've made 1,000,000 thaler from using trade caravans.
Keep 10 bundles of velvet in your inventory.
Complete the summer feast quest found in any village on the eastern side of the map.
Successfully blow a hole in a castle/town wall before a siege.
Build three upgrades in a single town/castle you control.
Finish the Cossack Hetmanate's main storyline quest "The Black Mace"
Finish the Polish Commonwealth's main storyline quest "The Deluge"
Finish the Moscovite Tsardom's main storyline quest "The False Dmitry"
Join the Crimean Khanate and eliminate all other factions.
Join the Kingdom of Sweden and eliminate all other factions.
As any faction; conquer the map and eliminate all other factions.
Kill 50 enemies with grenades.