GC1886 wrote:
and if that's corrected (genitive), is it 100% correct?

Grammatically, yes.

But I'm not sure if it's idiomatic.
Slí bheatha "way of life" is how you are getting the means of life, i.e. keeping yourself alive: your occupation, dein Beruf, not your "Lebensweg" in a broader sense.
Beatha (to answer your other post) is "life" in a more biological sense.
Saol (from Latin saeculum) is your life span on earth.
So: bealach (Weg), slí (Weg), cosán (Pfad) mo shaoil (of my life)
But the problem still is: I've never heard or seen this phrase used in Irish.
