The Greeks & Romans had multiple of myths about fierce boars running wild. Wild boars were common in ancient Greece and they made worthy opponents for Greek heroes and tools of vengeance for the gods. Adonis died after being gored by a wild boar and Aphrodite held him as he bled to death. In various versions of the Adonis story, his death is the revenge of a jealous god.
King Oeneus, the king who introduced wine-making to Aetolia (today western Greece), failed to properly honor Artemis. As punishment for his oversight, Artemis set the Calydonian boar on the region of Calydon in Aetolia, tearing up vineyards. Oeneus' name means "wine man". The story includes a heroine, Atalanta, who draws first blood. She also is the romantic interest to Meleager, son of King Oeneus. A tragic story comes from a fight over whether it is a disgrace to honor a woman hunter with the hide of the slain boar as a trophy.
"Atalanta and Meleager" by Charles Le Brun (1619–1690) from the Walker Art Gallery in the Liverpool, UK. This image is used under the terms of the Creative Commons Attribution Non-Commercial license (CC BY-NC).
Arpi, a Greek colony that minted coinage, shows the Caledonian boar on the reverse. The Greeks and Romans credit Diomedes, a participant in the Trojan war and a main character in Homer's Illiad, as the founder of Arpi. He was son of Tydeaus, who was the son of King Oeneus of Calydon. This origin story explains the Calydonian boar on this coin of Arpi.
"For not far above the sea (in the plain, at all events) are situated two cities, Canusium3 and Argyrippa, which in earlier times were the largest of the Italiote cities, as is clear from the circuits of their walls. Now, however, Argyrippa is smaller; it was called Argos Hippium at first, then Argyrippa, and then by the present name Arpi. Both are said to have been founded by Diomedes."
-Strabo, Geography, VI.3.9 
Map from "Coinage and Money under the Roman Republic", by Michael Crawford, showing the Greek colonies of Campania and Magna Grecia.
Apulia is modern Puglia in Italy and Arpi a mint in Norther Apulia. Livy reports that the Arpi made an alliance with the Romans during the Second Samnite War (326 - 304 BC) - supporting Lucius Papirius Cursor's advances in Apulia because they were tired of Samnite raids.
"The other army, under the consul Papirius, marching along the coast as far as Arpi, had found all peaceably disposed, more because of the wrongs done by the Samnites and the hatred they had engendered than owing to any favour shown by the Roman People."
-Livy, History of Rome, 9.13 
Greek, Northern Apulia, Arpi, circa 325-275 BC, Æ (20mm, 7.33g, 5h).
Obv: Laureate head of Zeus left; thunderbolt to right
Rev: Boar standing right; above, spearhead right,APΠANΩN in exergue
Ref: HN Italy 642
The Calydonian boar, more than two centuries later, appears on this Roman Republican coin of C. Hosidius Cf Geta. The boar in this case a complement to the obverse of Diana (the Roman equivalent of Greek Artemis). Hosidius likely a casualty of proscriptions by triumvirs after the death of Julius Caesar.
"there was Hosidius Geta, whose son arranged a funeral for him, as though he were already dead, and saved him in that way"
-Cassiud Dio, Roman History, 47.10.6 The son of Geta pretended to burn his father's remains in the courtyard of his house, making people believe that he had strangled himself. Then he conveyed him secretly to a newly bought field and left him. There the old man changed his appearance by putting a bandage over one of his eyes. After the return of peace he took off the bandage and found that he had lost the sight of that eye by disuse.
-Appian, Bellum Civile, 41.1 
Roman Republican, C. Hosidius C.f. Geta, 64 BC, AR Serrate Denarius (18mm, 3.97g, 6h), Rome mint
Obv: GETA – [III·VIR], draped bust of Diana right, bow and quiver over shoulder
Rev: C·HOSIDI C F.Calydonian boar standing right, pierced by spear and attacked by dog
Ref: Crawford 407/1;
C. Hosidius C.f. Geta, 64 BC, AR denarius (18mm, 3.77 g, 3h),Rome mint
Obv: Diademed and draped bust of Diana right, with bow and quiver over shoulder
Rev: Calydonian boar standing right, pierced by spear and harried by hound below
Ref: Crawford 407/2; Sydenham 903; Hosidia 1
The wild boar on this next Roman republican denarius is not the Calydonian boar, but rather the Erymanthian boar, of the 4th labor of Hercules.
Hercules and the Boar of Erymanthus, Antonio Tempesta (Italian, Florence 1555–1630 Rome), 1608, image public domain with thanks to the MET.
This coin from a set of 5 coins issued by M. Volteius that refer to the principal agonistic festivals celebrated annually in Rome. This coin refers to the Ludi Plebeii, held each year from 4 to 17 November. The Ludi Plebeii were held in the Circus Flaminius which was located near the temple of Hercules Magna Custos ad Circum (Hercules the Great Guardian at the Circus). The implication of the coins according to Crawford, is to advertise the largess that would have been provided had the moneyer been elected Aedile.
This Roman republican coin was issued during the time of the Sertorian War in Spain where Quintus Sertorius, an anti-Sullan rebel, battled against Pompey and Metellus.
M. Volteius M.f., 75 BC, AR denarius (19mm, 4.0g, 6h). Rome mint
Obv: Head of young Hercules right, wearing lion-skin headdress
Rev: Erymanthian Boar running right
Ref: Crawford 385/2; Sydenham 775; Volteia 2
During the Roman imperial period, sarcophagi depicting the Calydonian boar hunt were popular, perhaps to emphasize the heroic virtues of the deceased. (See: the Capitoline Museums)
Detail from sarcophagus depicting Meleager and Atalanta as Artemis. Capitoline Museums, Public domain, via Wikimedia Commons.