This is the safest method for the latest version. You can typically find the "PS Vita System Software Update" page on the official PlayStation website.
Whether you are looking to update a stock console or need a specific version for homebrew purposes, this guide covers everything you need to know about the and installation process. What is Psp2updat.pup? Psp2updat.pup Download
If your console has a weak Wi-Fi chip or you are in a location without internet access. This is the safest method for the latest version
On the Vita, go to > System Update > Update by Connecting to a PC . Method 2: Safe Mode Installation If your Vita won't boot properly: Turn off the device. Psp2updat.pup Download