Here is the full list of all 44 Song of Nunu: A League of Legends Story achievements.
Dream for the first time.
Dream for the second time.
Meet Braum, the Heart of Freljord.
Find the Jurlberry fruit.
Awaken the Kellurel.
Find the frozen wild yetis.
Activate Ramshara, the forgotten city.
Dream for the third time.
Survive the avalanche with Braum.
Free Willump.
Complete the Biggest Snowball Ever sequence.
Defeat Lissandra.
Complete the Epilogue.
Three booms in a short time are better than one.
Freeze a waterfall.
Enchant a krug.
Forge something with magic ice.
Hit a poro with a snowball.
Freeze an ice wolf.
Win a fight against multiple enemies without ever being hit.
Sneak into the Frostguard Citadel without being detected.
Win all the snowball fights against Willump.
Eat a bunch of berries offered by Willump.
Hug Willump.
Make Willump dance.
Throw a snowball into Willump's open mouth!
Break a snow figure made by Willump.
Enchant an Elnük with the Flute.
Help one sad Poro.
Help all the sad poros.
Find one mural.
Find all the yeti murals.
Find one stanza of the Notai Song.
Complete the Notai Song.
Meet Ornn, the Fire Below the Mountain.
Meet Volibear, the Relentless Storm.
Defeat 25 enemies with a finisher.
Activate 5 consecutive climb boosts.
Activate 20 boosts while sledding.
Complete the Ramshara drums sequence without failing.
Defeat 6 enemies using the environment.
Defeat 50 Frostguard soldiers using the biggest snowball ever.
Complete all sledding sequences without taking any damage.
Hit Ornn with a snowball.