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