Ah, alright thanks guys! I think I have confirmed that catching monsters from capture quests and the like add them to the arena, if they can be added.
Also, I have beaten all of the monsters in their time constraints (it's just super hard, haha) with my brother. For Baroth I suggest that someone guns, as the elemental shells (water + fire) work wonders. Use traps, set up bombs and use every single thing in your inventory to gank the hell outta them before you even think about attacking in a normal manner.
Hope this helps people too!