Since you were fully rooted you should know how to use adb, right? First, download the superuser .zip file from here
Superuser to be used for rooting after you flashed TWRP recovery (assuming this is what you're referring to with 2.2.2) - make sure oyu download the ARM superuser version (suggest 3.1.3 which works fine on all my devices).
Connect your TF300 to your PC and start it in fastboot mode (press power and Volume down buttons simultaniously until you get "OS will start coldboot if no input ..." in the top left corner; when this happens a second or so later you will see 4 square icons in the centre of the screen, use your volume down button to get to the 3rd USB icon and then press volume up to confirm. You will now be in fastboot mode.
open the command prompt on the folder where you have TWRP image blob (probably /android-sdk/platform-tools) and press shift+right click on it -> from the drop-down menu select "Open command window here". You now have cmd running in the right place.
type fastboot devices, which should return your device serial number if you have established communication with the TF300.
Next type "fastboot -i 0x0B05 flash recovery xxx-xxx-.blob" without quotes and where xxx is the filename you have for the recovery blob.
The flash should take around 5-10 seconds. When done power off (hold power button in until the screen goes blank) and press power + volume down buttons again until you get the comment "OS will start coldboot etc." and as soon this appears press volume up button this time; this will start the recovery you just flashed. Go to install and select the Superuser-3.1.3-arm-signed.zip you previously downloaded and dropped to your TF300 internal SD card root. Follow the necessary steps and reboot when done. YOu should now be fully rooted again with custom recovery.
