This is an annoying one due to Pure drops being hard to get.
Shards - Dropped by Prisoners and Crystal Lizards in 3-1, Bought from the Once Royal Mistress for 3000 Souls each.
Chunks - Kill the Babys Nail Black Phantom in front of the 3-1 Area Boss. 3-2 and 3-3 Crystal Lizard drops.
Pure - Drops from 3-2 and 3-3 Crystal Lizards.
Information gotten from http://demonssouls.wikidot.com/upgrade-moon