A road-rail tunnel (or a road tunnel) is a nonsense for the ventilation and safety issues aired above - one need only look at those horrific Alps road tunnel fires to know that you'd never choose to go down that route.
But for this to work, it would presumably need an HSR link from HS2 (Crewe?) across North Wales - presumably on or adjacent to the existing line and the A55, and then into a tunnel around Holyhead. 75 miles at a tunnel speed of 125 mph is 36 mins in the tunnel, with <10 miles into Dublin itself (8 mins?).
Holyhead to Crewe is about 105 miles (railmiles), so let's assume Celtic Shinkansen is the same distance and operates at 320 kph, giving a journey time of about 32 minutes to Crewe (76 mins to Dublin). Crewe to Euston is 58 mins, leading to <140 mins Euston to Heuston*.
<2h20 London - Dublin would certainly take much of the available traffic, but I don't know how many people actually travel between the two daily - hard to see 700+ seats every 30 mins (one express, one calling at Bangor, Crewe, Birmingham Intl, Heathrow) required.
(*I've no idea which Dublin station this would use, but Euston to Heuston amused me.)