Here is the full list of all 41 DARK SOULS: REMASTERED achievements. It takes around 60-80 hours to unlock all of the achievements on Windows.
All achievements completed. Congratulations!
Acquire all sorceries.
Acquire all rare weapons.
Reach "The Dark Lord" ending.
Acquire best weapon through magic reinforcement.
Acquire best weapon through divine reinforcement.
Acquire best weapon through lightning reinforcement.
Acquire best weapon through chaos reinforcement.
Acquire all pyromancies.
Acquire best weapon through crystal reinforcement.
Acquire all miracles.
Discover Darkwraith covenant.
Reach "To Link the Fire" ending.
Acquire best weapon through occult reinforcement.
Defeat the Soul Lord Gravelord Nito.
Defeat the Four Kings, inheritors of souls.
Acquire best weapon through enchanted reinforcement.
Acquire best weapon through raw reinforcement.
Discover Warrior of Sunlight covenant.
Acquire the Art of Abysswalking.
Defeat the Soul Lord Bed of Chaos.
Defeat Seath the Scaleless, inheritors of souls.
Defeat Crossbreed Priscilla, the Lifehunter
Acquire best weapon through fire reinforcement.
Defeat Dark Sun Gwyndolin, the Darkmoon God.
Discover Forest Hunter covenant.
Discover Blade of the Darkmoon covenant.
Acquire best weapon through standard reinforcement.
Discover Path of the Dragon covenant.
Discover Princess's Guard covenant.
Acquire the Lordvessel.
Arrive in Anor Londo.
Acquire the Rite of Kindling.
Discover Chaos Servant covenant.
Ring Bell of Awakening in Quelaag's domain.
Ring Bell of Awakening at Undead Church.
Discover Way of White covenant.
Discover Gravelord Servant covenant.
Arrive in Lordran.
Acquire Estus Flask.
Light bonfire flame.