Here is the full list of all 40 Hyper Knights achievements.
Start New Game+
Take over every Region
Defeat main Castle
Build 6 Overmap Buildings
Use every combo once
Hold 5000 Gold
Recruit 10 Knights
Defend a Convoy
Defeat 10 Roamers
Win a battle when outnumbered 3 to 1
Max out every Upgrade
Reach Level 150
Get an army of 200 units
Kill 50 units without taking damage
Unlock every Combo
Fight alongside 4 friendly Knights
Kill 30 units while in SUPER SELF
Max out a unit upgrade
Raid 10 Villages
Reach Level 50
Take 5 Castles
Kill 3000 units
Use SUPER SLASH
Win a battle versus 4 Knights
Win a battle involving 500 units
Use 100 Combos
Win a battle versus 150 units
Kill 15 units with a single combo
Fully upgrade 5 Castles
Reach Level 20
Max out one Combo
Fully upgrade 3 Outposts
Kill 100 units in a single battle
Defeat 10 Knights
Join a friendly Knight in battle
Fully upgrade a Village
Kil 200 units
Take over a region
Raid 10 Convoys
Stun 50 units