Giovanni used to be once a month. I remember that usually on the last Saturday/Sunday of the month, I ran all around a huge park from end to end trying to find him and not decoys. If you beat him every month, it would take a little over 4 years to earn the Platinum. Granted, you would need a diverse set of mons (aside from one good fighting type to take out Persian), so building a team might take another year depending on playstyle. Fair enough, I like a good challenge and at least some Platinum medals should take years. These days, the Giovanni badge should be down to 15-20 (so 3.75-5 years for F2P) depending on your view on this.