I know your issue has been sitting here unanswered for months now, so you might not need this information, but in case someone else comes around with the same problem:
I've had a similar issue - phone just went into a boot loop and I had some critical files to recover from internal storage.
Unfortunately, I'd never switched on debug mode in my phone before, so no ADB commands were an option, but Fastboot worked fine, and that eventually led to my solution.
For your phone, you'll need to use this TWRP recovery image and follow the instructions on that page - except for perhaps one instruction:
Where it says to type
fastboot reboot I opted to rather manually power it down and then disconnect. Then, I used my phone's Recovery Mode button combo to boot into TWRP. The reason for this, is that my phone's (and supposedly many other phones') system will automatically replace the internal Recovery upon boot. So, if you flashed it with TWRP and typed
fastboot reboot it'll go back into a boot loop (and also - invisibly to you - quite likely replace the built-in Recovery, meaning you'll have to repeat the flash operation).
So, in summary
- Download TWRP
- Start phone in fastboot mode (you'll have to Google to check how to do this for your device)
- Flash TWRP to Recovery partition using fastboot from a PC (this is the
fastboot flash recovery twrp.img command after confirming that fastboot works and communicates with your device via
- Power down your device
- Insert a large enough SD card to perform your backups
- Use the button combo to boot into Recovery mode (remember to not start up normally, otherwise you'll very likely have to flash TWRP again)
- Use TWRP's tools to backup your system (SEE CRITICAL NOTE BELOW)
- When you're done, power down, remove SD card (and make a copy of it somewhere else, lest you lose it)
The built-in backup on my device's distro of TWRP does NOT backup your actual user-generated data like downloads and pictures, BUT, the TWRP file manager does allow you to browse to all the different folders and manually copy those to another place, e.g. the SD card
I really hope that helps!