The 8th Amendment limits lawful abortion to situations where the life of the pregnant person is at risk. No law can be introduced that allows abortion in other situations without constitutional change. The Constitution can only be changed by having a referendum.
Successive Attorneys General have said that under the 8th Amendment no reform to the abortion law is possible.
According to the Supreme Court, the 8th Amendment means that abortion is lawfully available in Ireland only where there is a “real and substantial risk to the life, as distinct from the health” of a pregnant person (Attorney General v X  1 IR 1, p. 53). Thus, the Protection of Life During Pregnancy Act 2013 does allow for abortion in cases where there is a risk to the life of the pregnant person and the foetus is not yet viable (i.e. cannot yet survive outside the womb) (see explanation here).
The near-total ban on abortion imposed by the 8th Amendment means that we cannot legalise abortion in cases of rape, incest, or risk to health without repeal of the 8th.
The current understanding of the 8th Amendment is that it does not allow for abortion in cases of ‘fatal foetal anomaly’. While some legal academics argue that this interpretation is too conservative, it is the government’s understanding of the Constitution and attempts to pass law to allow for abortion in these cases have failed on that basis.
Therefore, for any change to be made to abortion law in Ireland the 8th Amendment must first be removed from the Constitution.