PokéBase - Pokémon Q&A
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Pretty much, all of them, if you use them correctly. Of course, Pokeballs, Cherish Balls, Premier Balls and Heal Balls ETC. are tough to use, but the others are good.

Since Mesprite is a legendary, things can get a little complicated. It has a 0.4% catch rate...

pikaxhu2 has given the obvious one, the Master Ball. There are very rare, so think before you use one. Quick Balls have a chance if you spend one turn using a move that doesn't KO it, but gets it HP red or close to red Yellow. Then use one.

Just read the summaries of the balls in your bag to find out their strengths, and work out a good strategy.

The other option is to trade. Also, you could use an ActionReplay code, or just plain old cheats from R4s.