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 Four Kings, inheritors of souls.
Acquire best weapon through standard reinforcement.
Acquire the Art of Abysswalking.
Defeat the Soul Lord Bed of Chaos.
Defeat the Soul Lord Gravelord Nito.
Acquire the Rite of Kindling.
Defeat Seath the Scaleless, inheritors of souls.
Defeat Crossbreed Priscilla, the Lifehunter
Defeat Dark Sun Gwyndolin, the Darkmoon God.
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.
Acquire Estus Flask.
Arrive in Lordran.
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 Blade of the Darkmoon covenant.
Discover Warrior of Sunlight covenant.
Discover Forest Hunter covenant.
Discover Darkwraith covenant.
Discover Path of the Dragon covenant.
Discover Gravelord Servant covenant.
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.