Here is the full list of all 20 STAY COOL, KOBAYASHI-SAN!: A RIVER CITY RANSOM STORY achievements.
Play as Kunio
Ride a UFO outside the UFO Shooting Stage.
Become friends with Ryuji.
Take out a Moyakun.
Take out one mid-boss.
Defeat an enemy with a level 3 special attack.
Choose a pursuit attack.
Play as Mizoguchi
Defeat a big boss.
Replay the game for a second time.
Obtain one character skill.
One character has all skills at level 5.
Trade out an equipped item for the first time.
Receive Ending E.
Receive Ending B.
Clear the game once.
Receive the True Ending.
All skills acquired for every character.
Collect all equippable items.
Clear the game within 30 minutes.