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