PSP Go! (N10XX) 5th PSP generation · Pandora Battery access: No · Downgrading possible: Yes · lowest Firmware: 6.00 · Permanent CFW patch available: Yes

From here you'll have different options to choose from:

Option 1: Install a permanent patchable 6.61 Custom Firmware via Infinity (with small brick risk)

Option 2: Install a temporary Custom Firmware (needs to be reactivated after reboot, no brick risk)

Note: You might consider installing a 6.60 CFW since most plugins,
themes and programms are not optimized for 6.61 as of yet!