Here is the full list of all 23 Hero and Daughter+ achievements.
Participate in the economy of the town.
Complete Heiti story
Beat king Maou.
Have over 1 Million G.
Beat the Demon.
See the special illustration for a love event.
Beat the Dark Lord.
Participate in the economy of the village.
Take possession of my home.
Summon a girl for the first time.
Ralph become level 1
The Village reach level 100.
The town reach level 100.
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
Go to the hot spring with a girl.