What model and year Mac? What is present macOS version?
Do you have enough free disk space?
If upgrading from macOS Sierra or later, your Mac needs 26GB of available storage to upgrade. If upgrading from an earlier release, your Mac needs up to 44GB of available storage.
Also uninstall any antivirus and "cleaning" apps before trying installing again.
Some users have problem with skipping upgrade versions and even not updating to the latest version of Big Sur. Thus if you are still at 10.14 I wouod upgrade to Big Sur (11) and then to Monterey.
Are you using File Vault to encrypt the disk? If so turn it off and then try after the de-encrypting is complete. That can take many hours. It may be better to manually remove the encryption and then try updating to Monterey again.
Try booting to Safe Mode. That boot up takes minutes and clears caches and other things. The try upgrading again.
How to use safe mode on your Mac - Apple Support