To change to version one run the self-update command and pass in the --1 flag. This will change composer to version one and now you can install your dependencies.
composer self-update --1
Once you have installed your dependencies, now you can run the same command and pass in --2 as the flag and this will switch back to composer version 2.
composer self-update --2
Switching Specific Version
You can also change to a specific version which includes the minor version number as well and it's like below.
composer self-update 1.10.22 composer self-update 2.1.3
Update and Revert Version
To update the composer to the latest version, simply run the "self-update" command, and to revert back to the previous version do pass in the --rollback.
composer self-update composer self-update --rollback
For anyone that's interested to use the preview version, the command below will allow you to get the pre-released version.
composer self-update --preview