Eventual accounts tell of bodies piled within the waters high enough to dam its flow, and the river running red with blood. So while Alexander is known to have repeatedly emphasized the importance of maintaining contact with the beach to his sub-commander on the left (seaward) flank, it is safe to assume a lot of action that day along all the water course in its 2.5 km travel through the narrow and hilly coastal plain that prevented the Persians, with their greater numbers, from outflanking the attacking Greeks.
Initially, Alexander chose what was apparently unfavorable ground to attack across (rough, briar choked, uphill) which was in fact a feint meant to pin and hold the Persian forces. This surprised Darius who mistakenly elected to hold position while Alexander then led the true attack personally on the right while instructing the Macedonian phalanx trained infantry, his main body, to make contact and just hold the main Persian army in check; thus in essence he advanced to take up a defensive posture. Meanwhile Alexander personally led the more elite Greek Companion cavalry against the Persian left up against the hills, and cut up the enemy on the less encumbering terrain generating a quick rout. After achieving a breakthrough, Alexander demonstrated he could do the difficult and held the cavalry successfully in check after it broke the Persian right. Alexander regrouped, then turned the body into the right flank of the Persian center, butchering Darius' body guard and under generals, provoking a panic and flight by that emperor himself, and causing a general rout. Any subsequent pursuit of Darius was delayed and generally impeded by the fleeing Persian troops and camp followers, although he managed to follow Dari