Traditionally it was to slay the Nemean Lion, which had a hide no steel or stone could penetrate.
The Nemean lion.
His punishment for the slaying of his wife and children was to labor for his rival Eurystheus. These became the Twelve Labors.
A bull that was said to breathe fire. The Cretan Bull was the property of King Minos, and this was the seventh labor given to Hercules by King Eurystheus.
The Nemean lion.
The Nemean Lion.
He wears the Nemean lion's skin.
Hercules' 3rd labor was to find the Ceryneis Hind. He did it for King Eurysetheus.
Hercules needed to perform twelve labors as a punishment for killing his wife and children in a fit of madness. Completing the labors was part of his penance to atone for his crime and prove his worthiness to the gods.
After the big Lion of Nemea, which Hercules killed as his first labor.
Hercules' tenth labor was to bring back the cattle of Geryon. This took place on the island of Erythia.
He does not have a symbol animal. However, his first labor was to kill the Nemean lion and since then he wore its skin.
I believe you are referring to the Nemean's Lion fur. heracle's first labor was defeating the Nemena Lion, and after killing it, Hercules took it's fur and wore it because it was impervious to attacks.