Here is the full list of all 53 The Mageseeker: A League of Legends Story achievements.
Escape from the Great City of Demacia
Explore the Dark Forest
Recruit Rukko and find information about Kara's whereabouts
Rescue Yops from one of Hesbeth's labs
Rescue Kara from the Mageseekers
Meet Morgana
Free the mages imprisoned in Glyndemere Headquarters
Destroy the Capelworth Headquarters
Visit Lux in Terbisia
Explore the Central Headquarters
Complete the assault to the Great City of Demacia
Get Morgana's vision
Stop the mage execution at Meltridge
End Hesbeth's experiments
Complete the game
Unlock a spell from Leilani
Unlock the Unchained Mode
Unlock all spells
Unlock all ultimates
Unlock all slots improvements
Pet the dog, Sam
Pet the horse, Azucarillo
Fight Garen at the beginning of the game
Defeat the Polar Lizard
Defeat the Giant's Helm
Defeat Rayn in Devineur
Defeat Wisteria in Devineur
Fight Morgana
Fight Rayn in Glyndemere
Defeat the Rattleclaw
Defeat Killan
Defeat Garen
Defeat Jarvan and Shyvana
Defeat Wisteria in Meltridge
Defeat Wisteria
Complete Ternmoat Headquarters assault
Complete Cypress Glen Headquarters assault
Complete Iffighain Headquarters assault
Complete Quickmoore Headquarters assault
Complete Cloven Dell Headquarters assault
Complete all secret lab raids
Complete the first enemy wave
Complete the second enemy wave
Complete the third enemy wave
Complete the fourth enemy wave
Defeat Nocturne
Use opposite magics 150 times
Copy abilities from enemies 200 times
Hook and whirl 100 times
Hook 10 times in less than 8 seconds
Kill 5 enemies at the same time
Find all Silverwings
Unlock all achievements