The Etruscans, who were most commonly associated with the 'Tyrrhenian' moniker, were a Villanovan culture located in northern Italy who were most prominent from 700BC until their eventual conquering by the Romans in 400BC.
They were located primarily within the Italian territories of Tuscany, western Umbria and northern Lazio. They were influenced culturally by Greece and the Phoenicians and are thought to predate the Roman Republic.
At some point in history, many peoples within the Mediterranean began to associate Etruria with the concept of piracy, similarly to how we do with Somalia in the horn of Africa today. While the majority of Etruscans were not engaged in acts of piracy, they somehow became attributed with an infamous myth in which Tyrrhenian pirates foolishly attempted to seize the God Dionysus in the Aegean Sea with the aim of raping him and selling him into slavery.
The Greek deity was having none of this, and despite warnings from some of the pirates' colleagues whom recognized him they attempted to press forward. Resulting in Dionysus riddling their ship with plant vines and wild beasts.
When the pirates attempted to escape the deities wrath, Dionysus had them turned into dolphins.
This myth speaks of Tyrrhenian pirates, with the region of Tyrrenhia frequently associated with the Etruscan, Rhaetian and Lemnian cultures of Antiquity.
An Etruscan vase depicting the transformation of pirates into dolphins
Of course the pirates in question could have been descendants of any of these peoples. Though the Rhaetians are widely thought to have been derived from the Etruscans anyhow as a people who fled the invasions of the Gauls and came to live in the Swiss Alps.
On the other hand and perhaps most plausibly, the Lemnian language is thought to be in the same language tree as Etruscan, with those speaking it being a people who lived on the isle of Lemnos in eastern Greece. Far from Etruria in northern Italy and the Alpine based Rhaetians as well.
Because Lemnos is located in the Aegean Sea, it is likely that it was the Lemnians who were being referenced in this myth. However, it's worth noting even still that the Tyrrhenian peoples in general were associated with piracy in Antiquity. Etruscans in general seemed to be looked down upon by neighbouring Rome and Greece and were remarked as a people commonly engaged in freebooting as a result.