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