Here is the full list of all 123 Cassette Beasts achievements.
Defeat a Rogue Fusion
Obtain a rumour
Sign up to the Rangers
Complete the tutorial
Obtain the Mothwing Glide ability
Unlock Kayleigh
Obtain Bansheep
Obtain Candevil
Defeat a Swarm
Defeat an Unstable Fusion
Defeat an Orb Fusion
Defeat 5 Rogue Fusions
Defeat 10 Rogue Fusions
Defeat 20 Rogue Fusions
Defeat 50 Rogue Fusions
Visit every part of New Wirral
Observe 120 different species
Obtain 10 different species
Obtain 20 different species
Obtain 50 different species
Obtain 100 different species
Obtain 120 different species
Obtain additional data on every species
Obtain a Beast-type bootleg
Obtain a Fire-type bootleg
Obtain a Plastic-type bootleg
Obtain a Plant-type bootleg
Obtain a Water-type bootleg
Obtain a Poison-type bootleg
Obtain an Astral-type bootleg
Obtain an Ice-type bootleg
Obtain a Lightning-type bootleg
Obtain an Air-type bootleg
Obtain an Earth-type bootleg
Obtain a Metal-type bootleg
Obtain a Glass-type bootleg
Obtain a Glitter-type bootleg
Obtain the Bulletino Dash ability
Obtain the Electromagnetism ability
Obtain the Diveal Swim ability
Obtain the Pumpkin Vine Ball ability
Obtain the Averevoir Flight ability
Get the Fusion Radar
Obtain a monster form thought impossible to find.
Investigate a rumour
Unlock Meredith
Unlock Eugene
Unlock Felix
Unlock Viola
Unlock Barkley
Remaster a tape
Start Kayleigh's quest
Clear 1 Landkeeper office
Clear 2 Landkeeper offices
Clear 3 Landkeeper offices
Clear 4 Landkeeper offices
Clear 5 Landkeeper offices
Meet Kuneko
Meet Kuneko at 1 altar
Meet Kuneko at 2 altars
Meet Kuneko at 3 altars
Meet Kuneko at 4 altars
Bring Viola to the shipwreck
Complete Kayleigh's quest
Complete Eugene's quest
Complete Meredith's quest
Complete Felix's quest
Complete Barkley's quest
Complete Viola's quest
Get to 5 hearts with Kayleigh
Get to 5 hearts with Eugene
Get to 5 hearts with Meredith
Get to 5 hearts with Felix
Get to 5 hearts with Barkley
Get to 5 hearts with Viola
Enter a romantic relationship
Solve the riddle of Morgante's song.
Reopen every station
Defy all odds in a place between worlds.
Defeat an ancient force brought back to full strength.
Defeat Lamento Mori
Defeat Heckahedron
Defeat Alice
Defeat Poppetox
Defeat Babelith
Complete Morgante's song
Overcome the essence of fusion.
Meet the one who dutily attends the stations.
Find a helping hand in a place far away.
Come face-to-face with a faceless being.
Meet the Travelling Merchant
Defeat Captain Wallace
Defeat Captain Skip
Defeat Captain Zedd
Defeat Captain Judas
Defeat Captain Clee-O
Defeat Captain Lodestein
Defeat Captain Penny Dreadful
Defeat Captain Gladiola
Defeat Captain Heather
Defeat Captain Buffy
Defeat Captain Cybil
Defeat Captain Codey
Defeat Ianthe and become a Ranger Captain
Choose a design for Harbourtown's sign
Help Sunny start a new life
Help Hoylake with his research
Defeat a ghost
Complete Frankie's training
Complete Vin's training
Complete 5 noticeboard quests
Complete 20 noticeboard quests
Complete 50 noticeboard quests
Complete 100 noticeboard quests
Obtain a rare sticker
Find yourself somewhere far away.
Open a door long since thought lost.
Try to sneak past a battler by jumping over their head
Win a battle before it starts
Win a battle while ghostly
Win a battle while Gambit is active
Bring Meredith to the mall
Prove your worth to a certain warrior.