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