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