Here is the list of what items are necessary to complete an AF+1.
Apollyon AF Materials
WAR Argyro Rivet
MNK Ancient Brass
WHM Benedict Yarn
BLM Diabolic Yarn
RDM Cardinal Cloth
THF Light Filament
PLD White Rivet
DRK Black Rivet
BST Fetid Lanolin
BRD Brown Doeskin
RNG Charcoal Cotton
SAM Kurogane
NIN Ebony Lacquer
DRG Blue Rivet
SMN Astral Leather
Temenos AF Materials
WAR Ecarlate Cloth
MNK Utopian Gold Thread
WHM Benedict Silk
BLM Diabolic Silk
RDM Ruby Silk Thread
THF Supple Skin
PLD Snowy Cermet
DRK Dark Orichalcum
BST Smalt Leather
BRD Coiled Yarn
RNG Chameleon Yarn
SAM Scarlet Odoshi
NIN Plaited Cord
DRG Cobalt Mythril Sheet
SMN Glittering Yarn