Travelling to Dalian from Dublin via Beijing. Staying only for 24 hours. Irish citizen.

You won’t qualify for the 72 hour free transit anymore because it allows the traveler to transit in one Chinese city. But if your total layover time in Beijing and Dalian is within 24 hours, and the next stop after Dalian is not Ireland, you can enjoy the 24 hr direct transit.

Sorry,Here are the details:

29th April Arrive Beijing 8:05
Depart Beijing 12:35
Arrive Dalian 14:05

30th April Depart Dalian 14:30

That needs a visa. It's more than 24 hours on Chinese soil.

But its within 72 hours?

72 and 144 hours transit without visa only allow transit in one city (or region). Your two stops in Beijing and Dalian immediately limit you to 24 hours in China. If you don't have a visa you must change your flights or you will be denied boarding at your origin.