I earned 21 Platinum Trophies so far. I actively worked for them for a while, but gave that up some two / three years ago. I now only shoot for the Platinum when I'm in love with the game and / or it doesn't require me putting in a huge grind into a part of the game I barely touch. As such my most recent Platinum Trophy was for The Witness.
My rarest Trophy overall is the Killzone 2 Platinum Trophy 'War Hero', with five more Killzone 2 trophies in my top ten rarest Trophies - 'Heroic Survivor' for completing all missions on Elite difficulty, 'Veteran Ribbon', 'Expert Ribbon', and 'Cross-training Ribbon' for receiving all medals, and 'Valor Grand Cross' for reaching the top 1% in the weekly multiplayer rankings. The Killzone 2 Platinum is also the one I am proudest of, because I feel like I had to put a decent amount of effort into it and was not just handed the trophies at random. It is also one of the few games I returned to for each DLC pack, so I also have it at 100%.
My second rarest Platinum Trophy also appears in my top ten overall rarest; 'Vector Sigma Victory', the Platinum Trophy for Transformers: War for Cybertron. It required a non-insignificant time investment into the multiplayer component, which I took no issue with as I still find the game's multiplayer to be the best third person shooter multiplayer I have ever played and definitely in the top five multiplayer shooters overall that I have played. War for Cybertron's multiplayer is criminally underappreciated and you should all be ashamed. :<
I'm also pretty surprised that the Platinum Trophy for The Last of Us is my third rarest Platinum Trophy and still edges into my top ten overall rarest Trophies. I had expected it to be much more common considering the popularity of the game.