You're gunna have to full-time Footwork, so melee damage will be low.
When I used to fight Sky gods on MNK I would start a Boost cycle when they would be popping soon. TP was built on the pots down below with Meteor Cesti.
After the initial 300 TP Dragon Kick, swap into Martial Knuckles and continue to SATA Howling Fist for the rest of the fight (while keeping Footwork up).
Dune boots help immensely for this type of damage dealing. STR and VIT mods on HF/DK.