Originally Posted by NewbieRunner

Yes, your baggage can be checked through. Since both Ireland and Cyprus are non-Schengen countries there's no need to go through passport control, and since Ireland is in EU no need to re-clear security either. However, the flight from DUB might park at an apron position and you will be bused to the terminal.

If your flight arrives at a gate you only need to walk to your departure gate on the same level. If it's bus arrival you have to go up to Level H.

MUC is a very efficient airport and you will be fine unless the incoming flight is very late.