By using the mail writer trick and via modifiying the correct database you can manually maintain your Trophies and basically do whatever you want.
Note: Syncing at your own risk!!
Tutorials & Guides Compilation
TropHAX (HENkaku only)
[Tutorial] How to hack and modify Trophies (none-henkaku)
Frequently Asked Questions
Can I get banned for doing this?!
We don't know how sony is going to deal with this yet. So its at your own risk.
My e-mail shows a [?] instead of the photo symbol?!
Try resetting the Vita's mail account or resend the mail.