After several game days of doing missions with "?" and "???" prizes thinking I'd get a Mystery Part as a prize, but instead recruiting a load of clients (I'd feel bad about refusing them! But I don't know how many I'll ever use anyway), I finally got a "search for Mystery Part" mission in Concealed Ruins. Of course, it was an escort mission. I'd just recruited Suicune, so I still had the stuff I found in Final Maze, which included no Reviver Seeds, so my idiot client went and got killed on the first floor. So I tried again and this time found the Mystery Part.
Happy about this victory, I went to Mystifying Forest to get Celebi and hopefully an Eevee. I recruited the second Eevee I found, and was excited when I got to Celebi's floor and started to go look for it, but then Moltres thought it would be fun to wander across the dungeon and toast Celebi before I even saw it. ._. A little later, I recruited a Flygon, and then I got to Darkrai's floor. Luckily, Darkrai happened to be in the same room that I spawned in. Unluckily, it was right across from Chikorita (and out of my sight), who of course loves to Razor Leaf everything in her way, and also is at level 78... at least Mystifying Forest is a pretty easy dungeon... but maybe I'll go in alone next time so I don't have to worry about my partners doing another legend-sniping spree.