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