If you want a Palworld-style instant success when fishing a monster, you can give the player a new monster anywhere you want by getting the first free party ID with amp_get_new_party_id / amp_get_new_box_id and then use amp_generate_monster to fill it with monster data. So when you successfully clear the fishing minigame you'd do this and then show a little announcement about it.
If you instead want to trigger a battle when fishing up a monster, the code in player_step_fill shows how to trigger a random encounter (though you'd probably wanna use a different list of monsters than the area's regular encounter table when picking which monster you fight).