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