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