Here is the full list of all 27 Great Hero's Beard achievements.
Defeat the Chubby Tubby Warlord
First Retirement
Defeat the Sea King Neposeitune
Defeat the Avalanche
Defeat Skelethrone King Slayer
Reach Level 100
Defeat Demon Lord Baal
Reach Level 80
Rescue Fifth Princess
Reach Level 60
Defeat the Guardian Azriel
Rescue 4th Princess
Rescue Third Princess
Reach Level 40
100'000 Damage
Deal 1M Damage
Deal 1'000 Damage
Rescue Second Princess
Reach Level 20
Rescue First Princess
200 ATK SPD
100 ATK SPD
100'000 HP
First Fusion
5th Retirement
10th Retirement
Max out all princesses