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