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 Rings Obtained
All Magic Spells Obtained
Obtain Istarelle
Deliver Makoto to Satsuki
Vanquish the Tower Knight without killing any archers
Embrace the power of the Old One
Obtain the Northern Regalia
Slayer of Demon "False King"
All Miracles Obtained
Rescue Yuria the Witch
Slayer of Demon "Penetrator"
Vanquish Penetrator with Biorr
Slayer of the Demon "Maiden Astraea"
Vanquish Maiden Astraea without killing Garl Vinland
Slayer of the Demon "Dirty Colossus"
Slayer of the Demon "Leechmonger"
Slayer of the Demon "Storm King"
Slayer of the Demon "Old Hero"
Slayer of the Demon "Old Monk"
Slayer of Demon "Maneater"
Slayer of Demon "Dragon God"
Vanquish Dragon God with the Hands of God
Give the Searing Demon Soul to Blacksmith Ed
Slayer of Demon "Flamelurker"
Slayer of Demon "Fool's Idol"
Vanquish the Fool's Idol without hitting any clones
Rescue Sage Freke the Visionary
Cross the walkway through the Idol's volleys of arrows
Slayer of Demon "Armor Spider"
Vanquish Adjudicator without having him fall down
Vanquish a player as an invader
Rescue Saint Urbain
Slayer of the Demon "Adjudicator"
Slayer of Demon "Tower Knight"
Help a player vanquish a boss
Slayer of Demon "Phalanx"