Here is the full list of all 20 STAY COOL, KOBAYASHI-SAN!: A RIVER CITY RANSOM STORY achievements.
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.
Play as Kunio
Play as Mizoguchi
Trade out an equipped item for the first time.
Defeat an enemy with a level 3 special attack.
Choose a pursuit 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.