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