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