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