Star Trek: 10 Strangest Alien Species
4. Tamarians
Tamarians represented a unique diplomatic challenge for anyone in the Alpha Quadrant. It's not so much that the universal translators couldn't figure out the language they spoke so much as it was what they were saying. Their sentences frequently came across as gibberish that made sense to them and no one else. Naturally, Captain Picard saved the day.
Dathon, a Tamarian captain, transported Picard and himself to the planet of El-Adrel IV, mostly against Picard's will. There, they fought together against a monster on the planet. While the beast killed Dathon, it turned out the shared conflict was chosen by him as a means of communicating with Picard. Dathon's plan was successful, if you ignore the fact he died.
Picard realized that Tamarians speak almost exclusively through cultural metaphors. The main problem with that was people who weren't Tamaranian didn't understand the metaphors without the context of being Tamaranian. But thanks to Dathon and Picard bridging the gap, the foundations of diplomacy were laid.