Things you can trade:
-Things with a MP sell value of 99 or less
Note that most Descended bosses and the like are worth low enough, but ult Descended bosses(See: LValk 6*+ forms, Goemon, etc), I think the Machine Gods(Hera, Zeus, Athena, Goemon), the rare invade Myth/Legend+ bosses(Think Another Justice, etc), and the like are changed to be 100MP to prevent tradability.
Notable things you CAN trade include MonHun evo materials, Pys, Kingtans, etc.