This is actually a Latin question but there was no option for Latin for some reason.
Let's break this down to make it easier. When struggling with a translation, I always find it helps to start a new line whenever you come across a full stop (or another sentence break in longer sentences). We can also highlight the main verbs.
Phaethon erat filius Apollinis.
Here, Phaethon is the subject of the sentence and his name is therefore in the nominative. However, there's another noun in the nominative in this sentence. Filius is a predicate nominative, as it is another noun which is linked to the subject of the sentence: it describes Phaethon. Next to the perfect form of esse - to be, we have 'Phaethon was a son'. But whose son? To figure this out, we look to the final word in the sentence: Apollinis. Here we have the genitive form of the name of the god Apollo, which in this instance has a possessive meaning. The line therefore means:
Phaethon was the son of Apollo.
olim Phaethon tristis erat
Here we have almost exactly the same structure as the first sentence. It has the same main verb and the same subject, Phaethon. Here we have a predicate adjective (tristis - sad) instead of a noun, but it is still doing the same job of describing the subject. The main difference is the word olim, which is setting the scene in a different period, one of a long time ago - olim means 'once' or 'once upon a time'.
Once, Phaethon was sad...
quod amici eum deridebant.
This second half of the sentence is a qualifier - it is telling us why Phaethon is sad. The quod (because) indicates this and creates a new clause. The subject here is amici (friends), and the main verb is deridebant (mock), in the imperfect tense. There is one more word - eum - which is the accusative masculine pronoun, and this tells us who the object of the sentence is: 'him', i.e. Phaethon.
...because his friends were mocking him.
‘pater tuus non est deus solis!’ dicebant.
As you can see, the first part of this sentence is direct speech, so that's nice and easy. The main verb outside of the speech quotes is dico - to say, and it is in the 3rd person plural active imperfect. This gives us an idea of who is speaking - it is the friends, who were characterised by the same tense and number in the last sentence. So what are they saying? The verb in the direct speech is est, but here it is qualified by non (not) and its subject also has a slightly more complicated predicate. pater tuus is the subject, which is the nominative form of 'your father'. Its predicate includes a noun in the nominative (deus), which is qualified by the genitive solis. If we put all these pieces together, we get: your father (subj) is not (verb) the god (predicate nominative noun) of the sun (qualifying genitive noun).