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.
Discover Gravelord Servant covenant.
Discover Way of White covenant.
Discover Warrior of Sunlight covenant.
Discover Princess's Guard covenant.
Defeat Crossbreed Priscilla, the Lifehunter
Reach "To Link the Fire" ending.
Defeat Dark Sun Gwyndolin, the Darkmoon God.
Defeat the Soul Lord Gravelord Nito.
Acquire the Rite of Kindling.
Defeat the Soul Lord Bed of Chaos.
Defeat Seath the Scaleless, inheritors of souls.
Defeat the Four Kings, inheritors of souls.
Acquire the Art of Abysswalking.
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.
Arrive in Lordran.
Acquire Estus Flask.
Light bonfire flame.
All achievements completed. Congratulations!
Acquire all rare weapons.
Acquire all sorceries.
Acquire all pyromancies.
Acquire all miracles.
Discover Blade of the Darkmoon covenant.
Discover Forest Hunter covenant.
Discover Darkwraith covenant.
Discover Path of the Dragon 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.