The company is tax "resident" in Bermuda, a British Overseas Territory.
In fact I'm not even sure what the Ireland connection is here except that there is a registered office in Dublin. It seems like all the action is taking place in Bermuda, so this is really a story about UK overseas tax havens.
The Irish part is there to allow it to funnel EU profits, and ireland allows for countries to be registered there, but not tax-resident.
Interestingly enough though, almost all of the zero tax places are British Crown dependencies, so presumably the UK government could exert pressure on them, if it really wanted to.
Again, for clarity, the Crown Dependencies are the Isle of Man and the Channel Islands. Bermuda is a BTO.
Bermuda has been self-governing since 1620. Britain has very little in the way of exerting any pressure on them short of imposing direct rule (which it seems to have done only twice: on Anguilla in 1968 after it was invaded and only partially on the Turks and Caicos in 2009-2012 due to systematic corruption).
They've been trying for a while. Ultimately, taxation is a national prerogative, and requires unanimity in Council, so it's unlikely to change any time soon.
Just for clarification, British Overseas Territories are not part of the UK. They set their own laws and manage their own internal affairs while their foreign relations and defence are managed by the UK.
In fact I'm not even sure what the Ireland connection is here except that there is a registered office in Dublin. It seems like all the action is taking place in Bermuda, so this is really a story about UK overseas tax havens.