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