He is variously said to have written 24, 30, or 44 plays, of which 19 titles are known: Adrastus, Aethon, Alcmeon, Alphesiboea, Athla, Azanes, Cycnus, Eumenides, Hephaestus, Iris, Linus, Moirai (Fates), Momus, Oedipus, Omphale, Philoctetes, Phrixus, Pirithous, and Theseus.
Achaeus of Eretria was regarded in antiquity as being the second greatest writer of satyr plays, after Aeschylus.
Some classicists suggest that the fact that he only won a single prize was due to his non-Athenian birth, as the men of Athens were loath to honour any but their own fellow-citizens.
The philosopher Menedemus thought his plays second only to Aeschylus, he was part of the Alexandrian canon, and Didymus wrote a commentary on him.
Athenaeus also claimed that Euripides took a line from Achaeus, while Aristophanes quotes him twice, in The Frogs and The Wasps.