Platinum hostesses are a tier of hostess that you can only unlock by successfully defeating the different Five Stars Clubs in Cabaret Battles (you begin with Yuki) - you earn one per club you successfully defeat. Prior to every Cabaret service, you have the option in preparation to complete Special Training with a Platinum hostess - these consist of multiple choice Q&A sessions and date minigames (such as darts, pool, Karaoke etc.). Answer the questions correctly and do well at the dates in order to boost the hostess stats, but this alone will not max them out - you'll need to use them in Cabaret Service to completely max out a given hostess. Expect between 20-30 services provided you're rotating them out to give them a chance to recover if their HP/Happiness begins dropping (as you should be).
While the other tiers of hostess max out at 30, Platinum Hostesses max out at 40. Also note that completing their final Special Training session will unlock a short substory, which you will need to do anyways if you are aiming for 100% completion.
The cabaret minigame is not especially difficult and gets easier as time progresses. Don't worry too much about the particular stats and aim to focus on the customer satisfaction level, indicated by a face to their left of thier table. Learn the hand signals and aim to have guests at Neutral as a minimum - you can put a hostess with an angry customer only very briefly, so you can buy yourself a few seconds if another hostess is finishing up with a guest.