Click on AP button, this will open up a file browser dialog. Select the recovery.tar created in step 2.
Put your Note 2 into Download mode by powering off your phone, and powering back on with the Volume Down + Home + Power key combination. Let go of the key combination when you see the device model logo (white text). Press Volume Up button when you see the warning.
Plug the phone in, Odin should have a Added! message displayed.
Click on the Options tab, and uncheck Auto Reboot. This is to prevent the phone from rebooting after the flashing. (Booting into OS will cause TWRP to be overwritten to stock)
Within Odin, click Start to start the flash process. Wait until done.
Press Volume Up + Home + Power key combination until phone reboots into showing device model logo and let go of keys. It should boot into TWRP.
Tap on Mount, and make sure storage is Internal storage
Plug the Note 2 into PC, open up a terminal and run adb backup --twrp
TWRP on the Note 2 should change into the backup GUI. Select the partition/root folder you want to backup and swipe to start the backup.
Warning: If you selected to backup /data, TWRP DOES NOT BACK UP THE INTERNAL STORAGE (/data/media/*)! User files are not backed up!
To back up stuff under /data/media, we do a adb pull /sdcard.
Tip: The folders under /data/media are all shadow reflexes of /data/media.