The Arena or The Forum was a battlefield that was located on Mount Olympus, more precisely at one of its edges and close to the Chamber of the Flame. That was probably the Gods' favorite location to watch and even participate in battles, which acted like a small coliseum. Two thrones, which likely belonged to Zeus and Hera respectively, could be seen at the middle of its bleachers, but apparently, Hercules was the Olympian who used and commanded the Arena more often, for his own entertainment.
Details of the Arena: there was an iron gate that was under the mentioned thrones from which warriors and enemies could march in; there were big statues of Goddesses on the walls and some walls had spiked vines that were overgrown.
The Forum of Hercules appeared in Ares' trailer for Ascension's Multiplayer and also in the Multiplayer Beta. In Ascension, the players fought each other at night while Hercules stood in the middle of the bleachers and watched the warriors fighting below him.
That map was used for the Multiplayer Mode Favour of the Gods, a free-for-all that supported four players in each match. Each player had to kill the other ones in order to gain the favor of the Gods. The player that had more favor - that is, the one who killed more enemy players - won the match.
Hercules' role in the match was to occasionally jump down and cause shockwaves with the Nemean Cestus that could damage the warriors and left them open to combos if they did not properly jump. Those shockwaves could also break the back walls of the arena and rung-out warriors while doing so.
Warriors could use the spiked walls that encompassed the arena to damage their opponents: if someone was kicked into one of the deadly walls, then they would be stuck there for a while.
A flurry of arrows could reign down from the sky if a warrior managed to get into the tunnel that served as the entrance for the arena and light the brazier; anyone who was outside when the hail of arrows started would be damaged severely. Normally, the said tunnel would have a large number of spikes that protruded out of the floor. Those spikes sometimes sunk back into the ground.
In the Trial of the Gods Mode of the Arena, Hercules acted as the boss of the level, instead of simply creating shockwaves occasionally. The player(s) must defeat him in order to win the match.
Kratos used the walls that were overgrown with spiked vines to defeat Hercules in order to retrieve the Nemean Cestus. After Kratos removed the Cestus from Hercules' hands, Hercules continued to attack him with his bare hands by grabbing, punching and throwing the statues around the Arena at him.
At a point near the end of the fight, Hercules threw Kratos to the edge of the Arena, which temporally stunned him, lifted its whole ground, and tried to make the Spartan slip and fall off, or simply made both him and the ground fall from the mountain. Kratos pulled himself back to the ground, jumped, and pounded the floor down again before he brutally smashed Hercules' face into the ground using the Cestus, and the last blow smashed the Arena's floor to pieces.
Kratos and Hercules (dead and gruesomely disfigured), tumbled into the sewers below, where Kratos left his half-brother's body to rot. Before he left, Kratos could take Hercules' Shoulder Guard that was found on the bottom of the water.
Kratos' fight with Hercules clearly shows, and uses, several aspects of the arena.