Herakles' Opponent(s)
I have not found any ancient references to the idea that Herakles [Heracles] invented pankration [pancratium]. Pausanias' Description of Greece 5.8.4, however, does mention that during Herakles' participation in the Olympic Games, the hero is said to have "won victories at wrestling and the pankration." The Roman writer Hyginus seems to be the only source for the name of who Herakles competed against in pankration, and he tells us in his Fabulae 273.5, that Herakles' opponent was called Achareus, who is otherwise completely unknown.
Hyginus is prone to making mistakes, which is probably why Paulys Real-Encyclopädie der classischen Altertumswissenschaft makes the point that a more famous character who was contemporaneous with Herakles might be intended in this passage, namely Aphareus. In addition to the name-similarity, Aphareus seems to be a good candidate here because of his familial connection to Pisatis, the region of Elis in which Olympia, the site of the Olympic Games, was located. Peisos [Pisus], the founder of Pisa—which was the capital city of Pisatis—was either a brother or a son of Aphareus.
One of the giants against whom Herakles fought together with the gods is incidentally called Pankrates, the "Almighty," which may or may not have anything to do with the sport of pankration.
A Brutal Bandito
About a generation before the time of Herakles and Theseus, a Phlegyan king of Elis named Phorbas, lived as a killer bandit haunting the road from Phokis [Phocis] to Delphi where he would attack pilgrims on their way to the oracle of Apollon [Apollo] at Delphi and force them to engage him in different sporting competitions. He was always victorious against them, after which he would decapitate the losers and hang their heads in the branches of an oak-tree which he had made into his home and "royal court of justice."
In his Images, Philostratus the Elder says that Phorbas competed with his opponents in wrestling, foot-racing, pankration and discus-throwing. Apollon, who was Phorbas' own grandfather, killed Phorbas in a boxing match. Since Phorbas would have died either before Herakles and Theseus were born, or, at the latest, when they were babies, Philostratus does not seem to think either of these younger heroes invented pankration.
Boycotting the Isthmian Games
Pausanias mentions a few different explanations for why the people of Elis did not participate in the Isthmian Games. The most famous has it that Herakles was unable, in battle, to defeat a powerful pair of twin princes from Elis, named Eurytos [Eurytus] and Kteatos [Cteatus]. During the celebration of the Isthmian Games a sacred truce was called during which Herakles ambushed and murdered the twins. Their mother Molione, according to the Description of Greece 5.2.2, "is said to have laid curses on her countrymen {the people of Elis}, should they refuse to boycott the Isthmian festival. The curses of Moli[o]ne are respected right down to the present day, and no athlete of Elis is wont to compete in the Isthmian Games."
A different account is reported in the Description of Greece 5.2.4, in which
Prolaos [Prolaus], a distinguished Eleian, had two sons, Philanthos
[Philanthus] and Lampos [Lampus], by his wife Lysippe. These two came
to the Isthmian Games to compete in the boys' pankration, and one of
them intended to wrestle. Before they entered the ring they were
strangled or done to death in some other way by their fellow
competitors. Hence the curses of Lysippe on the Eleians, should they
not voluntarily keep away from the Isthmian Games. But this story too
proves on examination to be silly.
Semi-Legendary Heroes
In the early 400s BC there were certain athletes who participated in the Olympic Games regarding whom claims of mythical proportions are made. Theagenes of Thasos, who took part in hundreds of competitions, was reputed to be a son of the god Herakles, while his opponent Euthymos [Euthymus] was said to be the son of the River Kaikinos [Caecinus].
Regarding Euthymos, the Description of Greece 6.6.5 says that
though he won the prize for boxing at the seventy-fourth Olympic
festival, [he] was not to be so successful at the next. For Theagenes
of Thasos, wishing to win the prizes for boxing and for the pankration
at the same festival, overcame Euthymos at boxing, though he had not
the strength to gain the wild olive in the pankration, because he was
already exhausted in his fight with Euthymos.
About six generations after Herakles' death the Olympic Games were discontinued before being revived later on in the reign of Iphitos [Iphitus] of Elis. Different sporting events were gradually reintroduced into the games over the course of several Olympiads. In the Description of Greece 5.8.8, when the men's pankration was finally readmitted
Lygdamis of Syracuse overcame all who entered for the pankration.
Lygdamis has his tomb near the quarries at Syracuse, and according to
the Syracusans he was as big as Herakles of Thebes, though I cannot
vouch for the statement.
How to Rebuild a City
There are many legends about Alexander the Great recounted in the tales which make up what is called the Alexander Romance. One of them refers to Alexander's destruction of Thebes after the city unsuccessfully revolted against him in 335 BC.
According to the Romance, the Thebans then inquired of the oracle of Delphi if they would ever be able to rebuild their home. The oracle replied that Hermes, Alkeides [Alcides] and Polydeukes [Polydeuces] would work together to cause Thebes to arise anew.
Later on, Alexander attended the Isthmian Games, over which he was invited to preside. Participating at the festival was a Theban named Kleitomakhos [Cleitomachus] who had enrolled in the wrestling, pankration and boxing competitions. After he won all the wrestling matches, Alexander promised to crown him personally and grant him any request if he conquered in the other two sports as well. The athlete achieved this and, upon coming to receive his prizes,
the herald demanded of him: "Tell me your name and from what city you
come, that I may announce you," he replied: "My name is Kleitomakhos,
but I have no city."
Presently the king addressed him: "Noble young man, you are a very
remarkable athlete. In one stadium, you have won three victories, in
wrestling, boxing, the pankration, and you have been presented by me
with three olive crowns, yet you have no city?"
Kleitomakhos answered: "I had one before Alexandros [Alexander] was
king, but he destroyed my fatherland."
Alexandros, knowing what he meant and what he was going to request,
said: "Let Thebes be rebuilt in honour of three gods, Hermes,
Herakles, Polydeukes, in order that this may be my free gift to you,
not your demand." So the oracle of Apollon was fulfilled...
And thus was Thebes rebuilt. I presume here that Hermes is supposed to represent wrestling, while Alkeides-Herakles stands in for pankration, and Polydeukes is the patron of boxing.
In Pausanias's account, the historical Kleitomakhos does indeed win in all such competitions but he does so more than a hundred years after Alexander's death. "At Olympia this Kleitomakhos was the first after Theagenes of Thasos to be proclaimed victor in both boxing and the pankration" (Description of Greece 6.15.3). The Syriac version of the Romance calls him Antimakhos [Antimachus].
