spoiler:

The base chance of encountering a shiny version starts off at 1%, increases by 1% after each kill streak milestone of 1,3,6,10,15,21,28,36 and 45, capping out at a 10% base chance with a kill streak of 45.

Hitting the woolzard with a fire element at least once in the battle increases the kill streak by 10 instead of 1.

At the moment, kill streak resets if you exit the void, not sure if it's intentional.

Each of the following items also increases this chance by 5% if they are in your active inventory, having all 7 would result in a +35% chance to encounter on top of the base rate.

Shepherd's Crook
Saladmandr Seed Pack
Bell Shell <= Info Subs
Aloha Pikazard <= Info Subs
Pikazard <= Info Subs » Frogzard Hunter Shop
Bulbazard <= Info Subs » Frogzard Hunter Shop
Doom Sheep