Here is the full list of all 40 Hyper Knights achievements.
Reach Level 50
Build 6 Overmap Buildings
Raid 10 Villages
Take 5 Castles
Defeat 10 Knights
Win a battle involving 500 units
Stun 50 units
Join a friendly Knight in battle
Max out one Combo
Fully upgrade 5 Castles
Reach Level 20
Get an army of 200 units
Defeat 10 Roamers
Fully upgrade 3 Outposts
Win a battle versus 150 units
Fully upgrade a Village
Kil 200 units
Take over a region
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 every Upgrade
Max out a unit upgrade
Reach Level 150
Raid 10 Convoys
Defend a Convoy
Win a battle versus 4 Knights
Use every combo once
Use SUPER SLASH
Kill 30 units while in SUPER SELF
Kill 15 units with a single combo
Start New Game+
Hold 5000 Gold
Win a battle when outnumbered 3 to 1
Fight alongside 4 friendly Knights