Learn Portuguese (Portugal): O gato daquela rapariga bebe leite.

Daquela is a contraction of the preposition de (of) and the demonstrative aquela (that). In Portuguese, when de comes right before aquela, they must squeeze together into one word.

How does daquela translate to "girl's"?

Portuguese does not use an apostrophe-S ('s) for possession. To say "that girl's cat", you have to flip it to "the cat of that girl". The de hidden inside daquela provides the "of".

Could I use dessa instead of daquela here?

Yes, but it changes the distance. Essa (and dessa) means "that" when the girl is near the person you are talking to. Aquela (and daquela) is used when the girl is further away from both of you, like "that girl over there".

Why do we need O at the start of the sentence?

Because Portuguese uses the "cat of that girl" structure, you need the definite article O (The) before gato. You are talking about a specific cat, so you literally say "The cat of that girl drinks milk".