I'd presume that you'd come off HS2 north of Crewe, and then run along the North Wales Coast on an HSR alignment, over to Angelsey and then into a tunnel? I presume it would be a little like HS1 north of the Thames where it weaves in and over rail and choob lines, A13, M25 and all the rest - if they can thread HS1 through that, then the North Wales coast is also possible.
The issues with that route (then as now) is crossing the Conwy estuary, getting past the mountainous headlands either side of Penmaenmawr, and then crossing the Menai Straits.
Here's an aerial photo of the Pen-y-Clip headland near Penmaenmawr:
Nearest the shore is the tunnel and viaduct of the current railway (the viaduct was built because the embankment kept washing out). Next is the 1930s road, now used as the eastbound carriageway of the A55. Then there's the old 1830s Telford road now used as a walking and cycle route. At the upper right you can see the exit of the 1980s tunnel that carries the westbound carriageway of the A55. It's rather crowded.
The Conwy estuary has a similar assortment of crossings: Telford's suspension bridge, Stephenson's tubular rail bridge, and a 1950s road bridge, as well as the A55 tunelling under the river. All in close proximity to a UNESCO world heritage site (Conwy Castle and Town Walls). If you go inland to avoid these, then you're going to run straight into Conwy Mountain and the Snowdonia National Park.
I've read the original report into the proposed route of the North Wales Expressway (as the A55 was called) in the 1980s: the recurring theme is of having to choose whether to run the road along the coast (destroying the views and cutting the seaside towns away from the shore) or plough through the mountains at great expense. The same choices would face a new high-speed rail route, with the added complication that the A55 is in the way now, too.
At the Menai Straits, there's been a desire for a third bridge to ease the road traffic situation for years. The fact that the waters of the straits are a Site of Special Scientific Interest has complicated the issue as it is. If a high-speed rail route were to come along, it would be strange to avoid Bangor, the most heavily used station in North Wales. But the current rail route into Bangor (tunnelling in and out across the valley) leaves you running parallel to the straits, which makes for a slow, tight curve onto a bridge to cross the straits.
Then again, why does the sea tunnel have to start at Holyhead? The road and current railway go there because Holyhead's harbour offers good shelter from the prevailing winds. That would be irrelevant if one were tunneling under the sea.
There's nothing impossible here though, it just requires some good engineering (and money) to overcome.