The individual components would be (roughly) “BAL-la AH-a CLEE-a” but you’d run them together, so that the second component would sort of disappear and it would come out like “BAL-la CLEE-a”. More or less.
Historically there were two settlements here: Baile Átha Cliath (“Town of the Hurdle Ford”) north of the river Liffey, and Dubh Linn (“Black Pool”) south of the Liffey. Dublin City got its English language name from the latter, but its Irish language name from the former.