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