Here is the full list of all 39 Showdown Adventure achievements.
Force Polewacy to give you diamond.
Defeat Homunculus.
Stay on the island.
Collect 3 diamonds.
Give Decard unidentified object.
Got a damage to over 550.
Defeat Snail.
Defeat Boss of all Bosses.
Got a damage to over 350.
Got a damage to over 250.
Have 10000 gold.
Got a character to level 15.
Got a damage to over 150.
Meet Decard.
Meet Nymph.
Kill 10 wild animals.
Meet Oldman.
Defeat Necromancer.
Got a character to level 10.
Give Mendzio bile.
Meet Mendzio.
Have 1000 gold.
Defeat Bug-Bros.
Combo over 150x
Combo over 100x
Meet Gimper.
Give Rojson mystic delta.
Defeat Witch.
Got a character to level 5.
Listen to the whole Rojson story.
Meet Rojson.
Meet Isanu.
Defeat 50 monsters
Combo over 50x
Defeat 25 monsters.
Open a treasure chest.
Got a character to level 2.
Defeat first monster.
Meet Polewacy.