Here is the full list of all 24 Royal Offense achievements.
Hire 666 dark heroes.
Kill weaken enemy.
Upgrade any weapons or armor to max level.
During single battle hire 300 heroes.
Build biggest castle in kingdom.
Hire 100 mages.
Get 10 Silver Medals on same mish.
Win any silver or gold level without any troops.
Headhunt for 10000 silver.
Hire 100 archers.
Get a diabolic number of Medals. ^T^
Get 5 gold Medals on same mish.
Level up any hero to level 9.
Kill a Troll, save the Lady.
Kill 3 enraged enemies.
Repair any building.
Hire two holy heroes at same time.
Level up any hero during mission to level 5.
Get 30 kills with just one unit or hero.
Earn 10000 gold.
Kill 50 rats.
Build 3 buildings.
Level up any hero during mission to level 3.
Get the first kill.