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
Defeat Skelethrone King Slayer
Defeat Demon Lord Baal
Defeat the Guardian Azriel
10th Retirement
5th Retirement
Rescue Fifth Princess
100'000 HP
First Retirement
200 ATK SPD
Reach Level 100
Rescue 4th Princess
Reach Level 80
100'000 Damage
Deal 1M Damage
Reach Level 60
Rescue Third Princess
100 ATK SPD
Rescue Second Princess
Reach Level 40
Deal 1'000 Damage
Reach Level 20
Rescue First Princess
First Fusion