Here is the full list of all 40 Hyper Knights achievements.
Fully upgrade 3 Outposts
Fully upgrade a Village
Kil 200 units
Join a friendly Knight in battle
Take over a region
Take 5 Castles
Raid 10 Villages
Defeat 10 Knights
Kill 3000 units
Kill 100 units in a single battle
Kill 50 units without taking damage
Use 100 Combos
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 5 Castles
Defeat 10 Roamers
Raid 10 Convoys
Defend a Convoy
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