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