Unlike the Lightning, Crystal, Occult, and Enchanted weapon upgrades, there is no Fire or Chaos weapon to be found, so you will have to make one from scratch.
This requires the Chaos Ember from the Demon Ruins and a total of 9 Titanite Shards, 10 Green Titanite Shards, 8 Red Titanite Chunks, and 1 Red Titanite Slab. Vamos in the Catacombs can upgrade a weapon to +5, then to Fire +5, then to Chaos +5.
This achievement requires upgrading a standard weapon to Chaos +5.
