"Мій тато - пенсіонер."
Translation:My dad is retired.
Technically I don't think it is correct to include retired as an alternative. To be a pensioner means that you receive some sort of economic benefit. It is possible to be retired without receiving any pension. Typically for professional athletes or any one else who retires early.
The primary message here is that Dad isn't working. I never heard someone called a pensioner until I taught English in Ukraine.