Here is a brief account of the battle given by the 5th century pagan historian, Zosimus, in his Historia Nova:
While Licinius was thus occupied, Constantine, who had a great number of transports as well as warlike vessels, and was desirous to make use of them in crossing over and possessing himself of the opposite shore, fearing that the Bithynian coast might be inaccessible to ships of burden, immediately constructed some small vessels, with which he sailed to the sacred promontory, which lies at the entrance of the Pontus, two hundred stadia from Chalcedon. He there landed his army, which, having done, he drew them up upon some adjacent hills. Licinius, though he then saw that Bithynia was already in the hands of his enemy, was rendered so desperate by danger, that he sent for Martinianus from Lampsacus, and in order to encourage his men to fight, told them that he himself would lead them. Having said what he thought necessary to encourage them, he drew them up in order of battle, and marching out of the city, met the enemy, who were prepared for him. A sharp engagement taking place between Chalcedon and the sacred promontory, Constantine had the superiority; for he fell on the enemy with such resolution, that of a hundred and thirty thousand men, scarcely thirty thousand escaped. When the Byzantines heard of this, they immediately threw open their gates to Constantine, as did the Chalcedonians also. Licinius after this defeat went to Nicomedia with what horse were left him, and a few thousands of foot. [Read more here.]And here is another account given by Eusebius in his Life of the Blessed Emperor Constantine.
And inasmuch as he who had lately fled before him now dissembled his real sentiments, and again petitioned for a renewal of friendship and alliance, the emperor [Constantine] thought fit, on certain conditions, to grant his request, in the hope that such a measure might be expedient, and generally advantageous to the community. Licinius, however, while he pretended a ready submission to the terms prescribed, and attested his sincerity by oaths, at this very time was secretly engaged in collecting a military force, and again meditated war and strife, inviting even the barbarians to join his standard, and he began also to look about him for other gods, having been deceived by those in whom he had hitherto trusted. And, without bestowing a thought on what he had himself publicly spoken on the subject of false deities, or choosing to acknowledge that God who had fought on the side of Constantine, he made himself ridiculous by seeking for a multitude of new gods. Having now learned by experience the Divine and mysterious power which resided in the salutary trophy, by means of which Constantine’s army had become habituated to victory, he admonished his soldiers never to direct their attack against this standard, nor even incautiously to allow their eyes to rest upon it; assuring them that it possessed a terrible power, and was especially hostile to him; so that they would do well carefully to avoid any collision with it. And now, having given these directions, he prepared for a decisive conflict with him whose humanity prompted him still to hesitate, and to postpone the fate which he foresaw awaited his adversary. The enemy, however, confident in the aid of a multitude of gods, advanced to the attack with a powerful array of military force, preceded by certain images of the dead, and lifeless statues, as their defense. On the other side, the emperor, secure in the armor of godliness, opposed to the numbers of the enemy the salutary and life-giving sign, as at once a terror to the foe, and a protection from every harm. And for a while he paused, and preserved at first the attitude of forbearance, from respect to the treaty of peace to which he had given his sanction, that he might not be the first to commence the contest. But as soon as he perceived that his adversaries persisted in their resolution, and were already drawing their swords, he gave free scope to his indignation, and by a single charge3177 overthrew in a moment the entire body of the enemy, thus triumphing at once over them and their gods. [Read more here.]