As stated here, but make sure there are no other specific things for upgrading from a version to another.
Upgrade CRDs
kubectl apply -f https://github.com/cert-manager/cert-manager/releases/download/v1.8.2/cert-manager.crds.yaml
Upgrade cert-manager
helm upgrade --version 1.8.2 cert-manager jetstack/cert-manager --namespace cert-manager
Check the pods
kubectl get pods --namespace cert-manager