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