Here's a list of quests including both side and main quests:
Act 1:
Enemy at the Gate
Mercy Mission
Breaking Some Eggs
A dirty Job
The Dweller of the Deep
Prisoner of Fate
The Caged Brute
The Marooned Mariner
The Siren's Cadence
The Way Forward
Act 2:
The Great White Beast
Einhar's Hunt
Einhar's Menagerie (unsure if this one counts)
Intruders in Black
Through Sacred Ground
Sharp and Cruel
The Root of the Problem
Deal with the Bandits
Safe and Sound
Shadow of the Vaal
Act 3:
Lost in Love
Victario's Secrets
Sever the Right Hand
Fiery Dust
The Gemling Queen
The Ribbon Spool
A Swig of Hope
A Fixture of Fate (easily missed because it is found in the archives rather than in town. Talk to Siosa near the waypoint)
Piety's Pets
Scepter of God
Act 4:
Breaking the Seal
Niko's Fuel (unsure if this one counts)
Niko's Mine (unsure if this one counts)
Niko's Explosives (unsure if this one counts)
An Indomitable Spirit
The King of Fury
The King of Desire
Corpus Malachus
The Eternal Nightmare
Act 5:
Return to Oriath
The Key to Freedom
In Service to Science
Death to Purity
The King's Feast
Kitava's Torments
The Ravenous God
Act 6:
Fallen from Grace
Bestel's Epic
The Father of War
Essence of Umbra
The Cloven One
The Puppet Mistress
The Brine King
Act 7:
The Silver Locket
Essence of the Artist
No Time like the Present
Web of Secrets
The Master of a Million Faces
In Memory of Greust
Queen of Dispair
Kishara's Star
Lighting the Way
The Mother of Spiders
Act 8:
Essence of the Hag
Love is Dead
The Gemling Legion
Reflection of Terror
The Wings of Vastiri
Lunar Eclipse
Solar Eclipse
Act 9:
The Immortal Syndicate
The Storm Blade
Fastis Fortuna
The Ruler of Highgate
Queen of the Sands
Recurring NIghtmare
Act 10:
Safe Passage
Map to Tsoatha
No Love for Old Ghosts
Vilenta's Vengeance
Death and Rebirth
An End to Hunger
Note that the Lord's Labyrinth quests do not count towards this achievement