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