Wyverne

You fight it in Plains Desert Border Special Area 4.

Its Nexomon's levels are rolled when the battle starts, from the story's difficulty plus this battle's own weight of 4, as the Battles page explains.

It's a wild battle that allows capturing, so the capture option shows and you can catch it. How likely a catch is is on the Nexomon page. Its Nexomon's levels are hidden during the battle.

What its boss cores do:

• A boss vitality core (150): 150% more max HP.
• A boss stamina core (250): 250% more max stamina.