Evolutions transcendences are defined at Scripts-->Data Mangling-->Database Setup-->Init Monsters, if you scroll to the right a whole bit you'll see this data:
(Basically it's an array of 3-member arrays, which represent the way to evolve, what thing triggers the evolution, and what monster to evolve to. For level evolutions, the trigger is the level to evolve at, for item evolutions it'd be the item ID, and so on... I'm unsure if I ever made item evolutions)
amp_clear_monster deletes a monster from the Active Monster Party (which is the big array that has all the monsters the player owns, including the storage boxes). Then you could use amp_generate_monster to create a new monster on the same AMP-ID, so it takes the exact slot the traded monster occupied. (Actually, you could just amp_generate_monster onto that slot directly, it clears the data with amp_clear_monster first). Once the monster is generated, you can manually apply unique quirks you want the traded monster to have (e.g. special moves or held items).
To get the AMP-ID of the monster to trade, I'd spawn a menu using msh_spawn_monster_list (which spawns a list of the monsters in the active party) which has a new "trade offer" menu event... it'd check if the monster in that slot matches what the NPC wants (that data would be stored in some global variables in the cutscene initialization script with the conversation) and if so, asks you a "ok?" question with msh_areyousure, and its OK script initiates the trade (sets the appropriate "trade done" flag, loads a different room with the trade animation, and then goes back).
If you need to familiarize yourself with how to carry data around, starting from mev_pause_monsters and looking into how the menus read party data further down the line should give you a good starting point in figuring out how to handle the AMP data (and the menu system in general).