Issues with upgrading project from Ionic 5 / Angular 12 to Ionic 6 / Angular 13

I am attempting to upgrade a project of mine to Angular 13 and I am running into a small issue when running this command:

ng update @angular/core@13 @angular/cli@13

I receive this error:

The installed Angular CLI version is outdated.
Installing a temporary Angular CLI versioned 13.3.7 to perform the update.
✔ Packages successfully installed.
Using package manager: 'npm'
Collecting installed dependencies...
Found 61 dependencies.
Fetching dependency metadata from registry...
                  Package "@angular-eslint/builder" has an incompatible peer dependency to "@angular/cli" (requires ">= 12.0.0 < 13.0.0", would install "13.3.7").
✖ Migration failed: Incompatible peer dependencies found.
Peer dependency warnings when installing dependencies means that those dependencies might not work correctly together.
You can use the '--force' option to ignore incompatible peer dependencies and instead address these warnings later.
  See "/private/var/folders/sk/s5rpkp151bn8mjblpzqbdw5r0000gp/T/ng-22f6Fq/angular-errors.log" for further details.

Is there something that needs to be updated first prior to updating Angular in my project for this upgrade to perform correctly?

npm i --legacy-peer-deps