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.
Discover Warrior of Sunlight covenant.
Defeat Dark Sun Gwyndolin, the Darkmoon God.
Discover Blade of the Darkmoon covenant.
Acquire best weapon through fire reinforcement.
Acquire best weapon through divine reinforcement.
Defeat the Soul Lord Gravelord Nito.
Acquire all sorceries.
Acquire the Rite of Kindling.
Defeat the Soul Lord Bed of Chaos.
Discover Gravelord Servant covenant.
Defeat Seath the Scaleless, inheritors of souls.
Defeat Crossbreed Priscilla, the Lifehunter
Discover Path of the Dragon covenant.
Discover Darkwraith covenant.
Defeat the Four Kings, inheritors of souls.
Acquire best weapon through lightning reinforcement.
Acquire the Art of Abysswalking.
Discover Forest Hunter covenant.
Discover Princess's Guard covenant.
Acquire the Lordvessel.
Arrive in Anor Londo.
Ring Bell of Awakening at Undead Church.
Discover Chaos Servant covenant.
Ring Bell of Awakening in Quelaag's domain.
Discover Way of White covenant.
Acquire Estus Flask.
Arrive in Lordran.
Light bonfire flame.
All achievements completed. Congratulations!
Reach "To Link the Fire" ending.
Reach "The Dark Lord" ending.
Acquire all rare weapons.
Acquire all pyromancies.
Acquire all miracles.
Acquire best weapon through standard reinforcement.
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 occult reinforcement.
Acquire best weapon through chaos reinforcement.