Catalina update still hasn

A typical update or upgrade can take anywhere from 15 minutes to an hour or more. It's dependent, in part, on whether you have a laptop or a desktop model, how fast the computer is, and how large the update/upgrade is. It is also dependent, in part, on how much free space is available on the target drive and how fast the drive is. You must be patient and let the update/upgrade finish on its own. During the update/upgrade, the computer may reboot several times. You should not interrupt the process before it completes the installation, after which is the last reboot which, usually, displays a login screen.

If you have already interrupted the process more than once, then it's possible for the installation to become frozen. If you do a forced shutdown and restart but cannot proceed beyond the login screen or the computer will no longer startup, then here's what you can try:

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button.

This will take quite longer than an update/upgrade because it attempts to reinstall the version of macOS that is already there. If that system is badly corrupted the process may take hours or may not work at all. If that is what happens, then you must erase the drive and start from scratch. You will lose all your data unless you have a recent backup.

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

If you have a complete backup of your old working system, then you can restore the backup from the Utility Menu rather than doing a fresh installation of macOS.

You cannot update from an earlier version of macOS to Catalina. Catalina is a major upgrade. If Software Update does not show that the upgrade is available, then you will need to upgrade it yourself. See How to upgrade to macOS Catalina.