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