You may be wondering why holding down the shift key doesn't work when so many instructions for Linux Mint and Ubuntu say that this is how you get to the GRUB Boot Menu. The answer is that there is a module that is required for this and Linux Mint 20 and I'd presume Ubuntu 20.04 and possibly other distributions derived from these apparently don't include it or it only works with systems that have a traditional BIOS. Most newer systems ship with UEFI and as such this doesn't work.
One answer to this is to wait until your UEFI/BIOS splash screen disappears and the normal Linux Mint boot process takes over. If you hold the left CTRL and ALT keys down and simultaneously tap the delete key in the upper right corner of most keyboards your system will reboot. This must be done before getting to the Linux Mint login screen. Once the system reboots you will see the GRUB menu. Press the up and down arrows to navigate to the menu entry you'd like to select. You only have about 30 seconds to utilize the up and down arrow keys on the keyboard before the system boots up normally so be ready to press these up and down arrow keys to stop the timeout from resulting in the system booting normally.
If you need to change a password simply select the advanced options for Linux Mint 20 and then select one of the recovery mode menu items from the next screen. You can also then select root option in the next menu that comes up next to Drop to root shell prompt. You will have to hit the enter key and then you'll see an actual prompt where you can type in a command. To change a password for a user simply enter the following command: passwd user_name [enter] and follow the instruction to enter the new password for this user twice. Reboot and you should be able to login using that user and your newly set password.