How do you catch mesprit when it is moving around so much?

Well, you should probably have a Pokemon in your party who knows mean look so Mesprit cannot escape. Stand on the boarder of Jubilife City's east side, then walk onto the route, then walk back into the city, etc, until Mesprit ends up on your route. Use a repel, and start to walk through the grass. The only Pokemon that will show up will be Mesprit.

Use mean look on mesprit, so it cannot escape. Try to weaken it down to 1HP, or as close as you can get it (I recommend using false swipe). Then just throw ultra balls at it. It takes a while. If you can't do it the first time, you can always try again. Status changes/afflictions are also good.

P.S: DO NOT LET IT FAINT!!! RESTART THE GAME IF YOU DO, EVEN IF YOU'VE NEVER SAVED IN YOUR LIFE!