Here is the full list of all 32 Eryi's Action achievements.
Be frozen solid.
Be rolled into a snowball.
Win easily.
Be electrocuted.
Be defeated by burning.
Go into Kerota's house.
Be defeated by fish-ramming.
Dodge the 3rd attack to the left.
Become a star.
Hit a spiky block.
Clear Stage 0.
Destroy a goal flag.
Be defeated by hot water.
Be defeated and declothed.
Be defeated by a metal dish.
Clear Eryi's Action.
Collect all the jewels.
Clear EX mode.
Become a snowman.
Drop a sprinkler in a spa.
Collect too many birds.
Hit a certain block too many times.
Swim through the middle of some water.
Pick up a fiery ghost.
Make a freezing device explode in the water.
Activate the secret spinning block.
Enter a command in the Artie fight.
Reset encroaching spikes.
Activate the electrobolt.
Enter a hidden floor.
Self-destruct in the Final Stage.
Clear EX mode with no defeats!