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