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