It's a complicated process, but yes, you can. The biggest obstacle is that you'll need a copy of the game on PS3 as well. Hopefully you got BL2 when it was free on PS+ a few weeks ago. If not, you can probably rent it somewhere for dirt cheap, or just borrow a friend's disc.
What to do:
- Copy your 360 save to your PC using Horizon
- Create a dummy save on the PS3 version, copy it to your PC via USB
- Get Brute Force Save Data and use that to decrypt the PS3 save
- Open your 360 save file in Gibbed's BL2 Save Editor, use it to change the save type to PS3, and overwrite your PS3 save (don't change the PS3 save's name)
- Back in Brute Force Save Data, encrypt the data and transfer it back to your PS3 via USB
- Wait for the cross-save patch to come out for PS3. In the meantime, make sure the file was correctly copied. Make a backup of it as well, just in case.
- When the patch is out, you will have your former 360 save running on your Vita.
For more info/help, check
this video and
this post.
Also, a caveat: your Badass Rank won't carry over, as it's saved in a different file. You may be able to transfer this file over as well using the method above.