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