What is the process for obtaining ETOPS certification for an engine or aircraft?
The engine manufacturer must get the certification for this specific model.
The aircraft manufacturer must get the certification for this specific aircraft with this specific engine
The operator company must get itself the certification, particularly the maintenance team.
The operator having been certified must get the certification every aircraft apart.
Certification is 90 min or 120min or 180 min
You don't certify the aircraft or the engine in isolation. ETOPS requires the airframe/engine combination to be certified as a whole. The combination must first meet the basic type certification requirements, then the operator of the aircraft must comply with the registration authority's rules for ETOPS operation in the country of registration.