MUSYNX

Here's the list of all the base songs :

Rhythm Fighter
Bunny Robbie
Little Red Riding Hood's Daily
Call me baby
TWINKLE STAR
Magic Squirrel Party
Welcome!
εν.στει Διον.σια
NEKOPARA
I LOVE MY MOTOBIKE
MUSE DASH
TriColour Heartbeat
TriColour World
Sparkle-Weaving Rain
Ba-Miao-Zhi-Yu
Distant time
Canon in D
Journey
LALALA Refrain
Beyond The Horizon
ANGER FORCE - STAGE 4 -
Koi
Mr. Rabbit
Gaokao.Love.100Days
That Little Starry Sky
ICEY
SanRenHeZouGe
Tears
Candleman
Gothique Resonance
Platina
GAMEBOY
CN Parents
Lost Memories
Banner of the Maid
Relishing Rain
Bass telekinesis
Confession
Doom Disco
Solar Wind
The Mountain Eater
Nick of Time
Silver Town
Annihilator
Africa
When You're Away
Luo-Chen-Huan
Su-San
Deities of Cathaysia
NiLangQianQiu
HaiTangXian
Sunsetting Billows
RPG Theatre
I will be failed
You Are Right
Burn
OPUS: The Day We Found Earth
8bit Adventurer
JOURNEY
8th Planet

If you have the Forever Friends DLC, make sure to uncheck it on Steam and select "Hide Unavailable" in-game to only see the base game songs.

Simply playing through all the songs on 4KEZ should get you the "Played Everything!" achievement.
Even though you need an average Sync of 115%, I would recommend getting at least 120% on almost every song to get the "MUSYNC" and "Heart-Sync" achievement.

If the achievements don't pop, restart the game and play through any song.