Here is the full list of all 30 Let's! Revolution! achievements.
Max out your Health.
Defeat the King with the Oracle.
Escape a level with 5 or more visible enemies.
Perform Premonition for 0 Energy.
Defeat the King with the Shadow.
Defeat the King with one health remaining.
Defeat the King with the Trooper.
Defeat the King.
Max out your Energy.
Hit 4 enemies with Roundhouse.
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 Charger.
Defeat the King with the Witch.
Defeat the King with the Hunter.
Complete a run without taking any damage on Normal or harder.
Defeat the King without stepping on any enemies.
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 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.