Monterey install stuck on less than a minute remaining

If still problem after waiting a long time, cancel the download and make sure there is not a remnant in the Applications folder (Install MacOS MOnterey).

Then boot to Safe Mode and try the download and installation while in Safe Mode. Booting to Safe Mode takes minutes.

How to use safe mode on your Mac - Apple Support

Note you need 26GB of free disk space to do the upgrade to Monterey.

As previous posting suggested after a reasonable amount of time has passed.

Also, consider some other factor that may come into play with the download.

There are factors:

1 - Like poor Wifi connection

2 - Slow wifi connection

3 - Too many other people downloading at the same time and Apple Severs are overloaded

4 - Software on the computer interfering with the download process including AntiVirus Software

5 - Running behind a VPN which may increase Packet losses and or corrupt the download

6 - If via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to your computer. 

7 - Best Results are via Ethernet Cable to Router

Patience and more of the same.

The upgrade can take some time. Just how long is difficult to predict.