Here is the full list of all 30 Let's! Revolution! achievements.
Maintain your Charge for 15 turns.
Hit 4 enemies with Roundhouse.
Defeat three or more enemies in one turn.
Max out your Energy.
Escape a level with 5 or more visible enemies.
Defeat the King with the Shadow.
Reach Beebom City.
Defeat a Heavy Guard.
Defeat the King with the Trooper.
Defeat the King.
Complete the tutorial.
Max out your Health.
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 Hunter.
Complete a run without taking any damage on Normal or harder.
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.
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.