I used Crobat and it worked really well. It's speed is high and it learns mean look at a pretty low level.
ok now you have to go to the lake by twin leaf town and use surf on the water there will be a cave go into it you ll see mespirt go bye it and push a it will make a noise and disseaper rown shows up and tells you to find it so you ll need to get the app from jublife city now get and use it there will be a bunny face (that's mespirt) folow it i know it ll go away to some where else you need the bike to get to it ok where you see it you got to go there and get to it before it goes some where else battle it oh ya and you need a move like scary face cuz it will run away got it? you need to use like 5 utra balls on it and its H P bar needs to be red and very low. if you put it to sleep you might need like three balls or just thorow a master ball. if you do all that youll have mespirt ta da!
GO to the Poketch marker app, then fly to eterna city.make sure to stock up on at least 5 dusk balls and 5 timerballs. just walk between eterna city and the route beside it until mesprit/cresselia appears. I made my level 40 kricketune use false swipe, and when it flees, try again, until its HP is down to 1 or close to 1. then catch a golbat at victory road. after that fly to eterna city and walk between the routes again, until mesprit/cresselia appears. let your golbat hold the quick claw and use mean look on mesprit/cresselia. then use your poke balls. don't worry if it isn't nighttime, I caught my mesprit in a dusk ball even though it was daytime. status problems are optional; but they increase the chances of catching them. hope I helped :)
Chat with our AI personalities
Yes, and here's how: get a Wobbefet or Dugtrio from either LeafGreen or FireRed. Then, find Mesprit using the poketch app. Have Wobbefet or Dugtrio first in your party, and battle it until it gets to red hp, and if possible, paralyze it. Keep throwing ultra balls at it, and eventually you will catch it. Here's why it works. Dugtrio and Wobbefet both have abilities which don't allow Mesprit to flee. You can also have a Golbat/Crobat and use mean look, but the method above works best. Note: this method can also be used for catching Cressilia.
jiroxy ball...
After you beat the elite four and the galactic biulding
You have two chances to catch Mesprit. If you accidentally make it faint both times, you can't catch it anymore. If you made Mesprit faint once, find it, trap it, lower its hp to 1 using false swipe (you should have gotten the TM), let it escape, then encounter it again and use a quick ball.
A Master Ball