"Master of PR Magic" and "The Master of PR Magic" are correctly capitalized. Whether or not to use "The" is optional and doesn't matter much. "Master of PR Magic" suggests that it is a title granted to anyone who can earn it. "The" suggests that it is unique, one-time, there is only one such person with that title. I probably would not use it, because on a real trophy it is more likely that it would not be used. But since it's a half-joke, it doesn't matter, and your friend will be delighted, no matter what it says exactly.

I would say # 2 is the best. You want to capitalize the first article in any sentence but an article or small preposition "for" or "of" don't need to be capitalized. Another option is to capitalize everything!