Wadtail

When it appears

As a tier-2 Nexomon, it only turns up in the grass after you beat Jin in Magma Grotto Town, in the main quest Tyrant Mulcimer, or from the start in Custom Mode with high-tier encounters allowed.

Capturing

Its favourite foods are Banana, Cream Puff and Flan, Wadgon's, as every stage of a line shares the first one's. Feeding it one adds 7 to your capture chance, where other food adds 2. As a dragon, it's harder to capture: food counts for less, Nexotraps count for half, and wearing it down adds at most 15 instead of 20. A Golden Nexotrap still adds the full 100. Catching a Nexomon explains how the whole chance adds up.