Here is the full list of all 25 Solune achievements.
Bet on the Imp in the Parwan Monster Races, and win.
Defeat Kenzan as Vaster in their first encounter.
Defeat both of the brothers who robbed Kandaria Castle.
Defeat Elrion in your first encounter.
Learn the truth of what happened to Kenzan's parents.
Have your pet dragon obtain the ultimate element.
Help fully rebuild Tenton into a bustling city.
Recruit a certain secret character.
Reach Rank 10 in the Parwan Arena.
Complete all 50 puzzles in the main game.
Enter the secret Puzzle Mode.
Enter the secret Developer's Room.
Beat the game.
Defeat Sol in his prison.
Find every treasure in the game, then go and show the Treasure Hunter in Tenton.
Beat the game, getting the 'good' ending.
Defeat the memory of the King of Dragons.
Hatch a Dragon Egg.
Obtain the Lightning element for your pet.
Obtain the Ice element for your pet.
Obtain the Wind element for your pet.
Recruit Striager (and Kenzan).
Obtain the Water element for your pet.
Obtain the Fire element for your pet.
Obtain the Shadow element for your pet.