This is an annoying one due to Pure being hard to find.
Shards of Darkmoonstone - Dropped from Crystal Lizards near Sparkly the crow in 4-1, Reapers in 4-2 and can be purchased from Graverobber Bilge in 4-2 for 3000 souls.
Chunks of Darkmoonstone - Dropped from 4-1 Crystal Lizards, 4-2 Reapers, the Uchigatana Black Phantom guarding Saint Urbain and the Crystal Lizard in 4-2 near the White Bow.
Pure Darkmoonstone - Can only be gotten from Crystal Lizard drops in 4-2 and 4-3 unless you get one from another player.
Information gotten from
http://demonssouls.wikidot.com/upgrade-crescent