Translation:He studies emergency medicine.
I've been wondering about this in general... could it be because it's immediately followed by a slender vowel in a collocation? It definitely shouldn't be slender in isolation, but because (I imagine) leigheas éigeandála is a more-or-less fixed phrase, maybe it's common to carry over the agreement across word boundaries.
The discussion above is referring to an old recording by the previous speaker, but in support of Pookagar's point, the Ulster equivalent of cad é does use a slender d, and is sometimes written goidé because of that.
But leigheas éigeandala is fairly modern phrase, and shouldn't really have devolved in the same way.