Here is the full list of all 37 Demon's Souls trophies - there are 22 bronze, 9 silver, 5 gold and 1 platinum.
All Trophies Obtained
All Magic Spells Obtained
All Rings Obtained
Obtain the Northern Regalia
Embrace the power of the Old One
All Miracles Obtained
Vanquish Penetrator with Biorr
Obtain Istarelle
Slayer of the Demon "Maiden Astraea"
Vanquish Maiden Astraea without killing Garl Vinland
Deliver Makoto to Satsuki
Vanquish Adjudicator without having him fall down
Vanquish the Fool's Idol without hitting any clones
Cross the walkway through the Idol's volleys of arrows
Vanquish Dragon God with the Hands of God
Give the Searing Demon Soul to Blacksmith Ed
Vanquish the Tower Knight without killing any archers
Slayer of Demon "False King"
Rescue Yuria the Witch
Slayer of Demon "Dragon God"
Slayer of the Demon "Storm King"
Slayer of the Demon "Old Hero"
Slayer of the Demon "Dirty Colossus"
Slayer of the Demon "Leechmonger"
Slayer of Demon "Penetrator"
Rescue Saint Urbain
Slayer of the Demon "Old Monk"
Slayer of Demon "Maneater"
Vanquish a player as an invader
Slayer of the Demon "Adjudicator"
Slayer of Demon "Fool's Idol"
Rescue Sage Freke the Visionary
Slayer of Demon "Flamelurker"
Slayer of Demon "Armor Spider"
Slayer of Demon "Tower Knight"
Help a player vanquish a boss
Slayer of Demon "Phalanx"