Here is the full list of all 22 Royal Bounty HD achievements.
Gain 10000 Ghosts
Win 10 battles using spells only
Gather all possible spells in the game
Use each spell in the game, at least once
Win a fight using one unit only
Have all 6 empty army slots
Use the summon spell 10 times in one combat
Save the dragon from the slaver's market
Fly the dragon
Leave Draco with Jaffar
Build a ship and sail off from Dadhab
Run from the prison guard
Reach Rockland
Reach Desertia
Reach Tundria
Enter the teleport at the end of the secret room
Reunite with Draco
Complete the puzzle map
Don't lose the Druid to activate the monolith
Complete the game on Easy difficulty
Complete the game on Normal difficulty
Complete the game on Hard difficulty