I haven't had a lot of experience with patching ISOs, though I do have experience with custom firmware to use for making legitimate backups of ISOs, using custom themes, etc. Hopefully I can help to at least you get started with the process.
You're going to need to install some custom firmware first if you haven't already. You're going to need to do that if you want to make a legitimate rip of the ISO of your copy of Valkyria Chronicles 3. You're also going to need CFW anyways in order to run the patched ISO, regardless of how you got it. The steps you take to install CFW on your PSP is going to depend on the model you have. The PSP1000 is the easiest for this part. The PSP2000 is fine, though I've heard there are a some differences in the earlier and later PSP2000 models that need to be taken into consideration when installing your chosen CFW. From what I've read regarding the PSP3000 and PSPGo, they're a bit less than ideal for fiddling with.
As for the firmware to use, I use 6.60 PRO-C on my PSP1000.
If I didn't explain things well enough, please feel free to ask more questions.
I hope I'm not too late to be of any help.
