Installing macOS: Disk with a mount point is required. Quit the installer to restart and try again.

It would help to know the exact model of your Mac and the current OS installed. You can get this information by clicking on the Apple menu and selecting "About this Mac" or by entering your serial number here:

https://checkcoverage.apple.com/

How are you trying to install Catalina?

Try creating and using a bootable macOS 10.15 Catalina USB drive using these instructions:

https://support.apple.com/en-us/HT201372

Edit: It may also indicate you have a corrupt file system or failing drive. Boot into Internet Recovery Mode (Command + Option + R) or from the macOS USB installer to run Disk Utility First Aid on the drive.

It might be pertinent to know why you are upgrading macOS.

If you can still boot into macOS, then you can create the bootable macOS USB installer. Unfortunately Apple doesn't provide the ability to create a USB installer on non-Apple operating systems or even on Macs which cannot run those versions of macOS.

You may need to first try upgrading to macOS 10.13 High Sierra, then finally upgrade to Catalina. You can find the links to macOS 10.13 within the Apple article I linked previously for creating the USB installer.

By initiating the macOS installer upgrade process from within macOS itself maybe some third party app/driver is interfering with the process. You could try booting into Safe Mode to initiate the installer. Personally I would go with the USB installer since it greatly reduces the risk of third party software interfering.

Keep in mind Catalina no longer supports 32 bit apps so you should either make sure your third party 32 bit apps are already upgraded to 64 bit versions or uninstall the 32 bit apps before upgrading.

https://support.apple.com/en-us/HT208436