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