Hey!
1. Install custom firmware.
2. To make it easy download a file called Autoplugin 2 to your vita in .vpk format.
3. Use VitaShell to click on the .vpk and install it.
4. Launch Autoplugin 2 and install two plugins "reVita" and "DS4Vita".
5. After reboot, you can press Start + Square to open reVita and create a rule to set "Analog Stick" to "Disabled", then set current profile to default across all apps. It might also disable your controller's analog stick but there's also settings in reVita for adjusting Analog Deadband and more plugins on Autoplugin 2 called "Disable Left Joystick" etc.
6. To pair your Dualshock 4 just go into the settings app on Vita and hold Share + PS while scanning Bluetooth Devices.
7. If you want to use your 8bitdo controller you have to install a plugin called VitaControl on Github, seperate to Autoplugin 2.