Give your suggestions and how you caught mespirit here

Well there are a ton of ways to do it, but the easiest IMO in DPP is to get a Murkrow. They appear at a higher level, learn mean look and have immunity to Mespirit's psychic attack. However the best pokemon to do this will always be smeargle in my opinion, spore, mean look, false swipe, and recover. Anyways, get a pokemon that knows Mean Look/Block, got to an area that has 2 routes close together with tall grass. Go back and forth between the routes, stopping to check if mespirit is in your area on the map marker app you get from the poketch company. Once you see it there go to the grass and find it. Mean look it so it can not flee, and do what you would normally do from there. However if the pokemon you have is switched out or faints without baton passing the mean look mespirit can flee. If you use a quick ball, use it turn one-five with a 4x catch rate, after every 5 turns it goes down to 3x, 2x, etc. After that use dusk ball at night or ultra balls will work somewhat well during the day.

Hope this helps, oh and here is a reallllly annoying guys video on how he did it.

For Pearl, you can replace Murkrow with Misdreavus/Mismagius, which is what I used (since they also get Mean Look). They're immune to Swift and have alright HP so you can just take hits and heal every now and then. Plus, Shadow Ball can take off a significant chunk of its health without killing it if you're not that high-leveled. (That was my strategy, anyway. I don't know how well it'd work for somebody else.)

I heartily recommend hunting it at night, as Dusk Balls are lovely. Since the battle will probably take a while, I'd pack some Timer Balls too. Just watch out for Struggle.. it'd kinda suck if you dragged the battle on so long that it ran out of PP. :p

I just threw my Master Ball at it On a somewhat related topic, I'm now trying to catch Cresselia, so...any advice?

That is exactly what happened to me. For both of us: Any ideas?

Well. First use the Pokemon recommended by the Users above. If you are playing Platinum, you will defeat the game before trying to catch it. If you can gain access to a Sableye with Mean Look, or I used a Wobuffett do do the bulk damage, they will really help, as Sableye is immune to both its moves. If youre looking for a good area to run in, then turn you Poketch on and run between Oreburgh and the non-cycling-road part of Route 206. Eventually the Cresselia (and Legnedary Birds) will arrive. Hunting at night is useful. However if it flees at low health, then bring a Quick Ball, cause they are useful.

Hope this helped!

My style for Mesprit/Crsselia was quite different to what is here lol

I had a fast pokémon in first slot (doesn't matter which as long as it learns mean look/hypnosis and is faster than the two) and used hypnosis. Then I brought out Pachirisu and used superfang 3 or 4 times before switching back to my hypno pokemon and using mean look (as it hadn't woken up yet) before bombarding it first with ultra balls before using timer balls.

I am in the process of catching Moltres, Zapdos and Articuno and will probably be using dugtrio with its ability Arena Trap this time around. I have 6 of them at L60 so I am set for it lol.

QUEEEEEEECK BAAAAAAAALLLLLL