Here is the full list of all 30 Let's! Revolution! achievements.
Defeat the King with the Trooper.
Defeat the King.
Defeat three or more enemies in one turn.
Hit 4 enemies with Roundhouse.
Reach Beebom City.
Defeat a Heavy Guard.
Complete the tutorial.
Unlock all skills and items.
Defeat the King with the Charger.
Defeat the King with the Oracle.
Defeat the King with the Witch.
Defeat the King with the Shadow.
Defeat the King with the Hunter.
Escape a level with 5 or more visible enemies.
Complete a run without taking any damage on Normal or harder.
Max out your Energy.
Max out your Health.
Defeat the King without stepping on any enemies.
Defeat the King with one health remaining.
Catch the King without killing any enemies.
Defeat the King on NG+5.
Hold 100 gold.
Hit 6 enemies with Armageddon.
Maintain your Charge for 15 turns.
Hit an enemy for 5 damage.
Perform Premonition for 0 Energy.
Perform a Slash for 0 Energy.
Hide 4 enemies with a Smokebomb.
Finish a run on normal or harder in under 10 minutes.
Recieve a complimentary Bubbleship Ticket from Chovy.