Here is the full list of all 23 Hero and Daughter+ achievements.
Take possession of my home.
Participate in the economy of the village.
Summon a girl for the first time.
Ralph become level 1
Participate in the economy of the town.
The Village reach level 100.
The town reach level 100.
Have over 1 Million G.
Beat the Dark Lord.
Beat the Demon.
Beat king Maou.
Complete Heiti story
Complete the soldier story.
Complete Hans story
Beat the secret bounty on the head of Maou
Beat the bounty creature from the otherworld.
Beat the monster house monster over level 100.
Beat level 100 of the Challenge Tower.
Beat level 1000 of the Challenge Tower.
Beat level 9999 of the Challenge Tower.
Reach level 999
See the special illustration for a love event.
Go to the hot spring with a girl.