Here is the full list of all 21 Lionheart achievements.
Complete all achievements in Lionheart
Survived the first battle
Mariabell joins the party
Sister Emma joins the party
Kite joins the party
Kagura joins the party
Sheela joins the party
Cid and Io join the party
Roux joins the party
Alexios joins the party
Accepted first Request from shop
Crafted the first equipment in shop
Crafted the first non-tutorial Emblem through alchemy
Crafted a 12 MP Emblem with MA++ and a ++ Skill
Fulfilled 6 requests in store
Defeated 100 Goblins
Defeated 999 enemies using front-line fighters
Defeated the Phantom Demon King
Defeated the strongest dragon
Destroyed the goblins' ultimate weapon
Cleared the game