The text commented on is from Arrian about the cavalry engagement after Gaugamela when Alexander was pursuing the fleeing Darius and there was a bottleneck of troops on the road up to the mountains.
Arrian uses the term "he himself", "Alexander himself", "Philotas himelf", "Hephaestion himself" etc a lot in his narratve. He seems to use it to indicate the importance or high rank of the person he is mentioning, as well as to indicate that that he believed it actually happened as his sources all agree about it. He also seems to be using it to say that these men, particularly Alexander, actually put themselves in danger in doing things rather than stand back and command from the sidelines.Then ensued the most obstinately contested cavalry fight in the whole engagement. For being drawn up by squadrons, the foreigners wheeled round in deep columns, and falling on Alexander’s men face to face, they no longer relied on the hurling of javelins or the dexterous deploying of horses, as is the common practice in cavalry battles, but every one of his own account strove eagerly to break through what stood in his way, as their only means of safety. They struck and were struck without quarter, as they were no longer struggling to secure the victory for another, but were contending for their own personal safety. Here about sixty of Alexander’s Companions fell; and Hephaestion himself, as well as Coenus and Menidas, was wounded.
In this particular instance, as pointed out in the post above, Hephaestion commanded the royal bodyguard squadron. I think the post misses the point though in that Arrian is saying here that the fighting was so heavy that the Persians got through the royal bodyguard. Hephaestion, as a Royal Bodyguard as well, would have been fighting beside Alexander. The Persians therefore almost got through him too, and almost took out Alexander. Hephaestion was later awarded a golden crown. These were awarded for valour and so there may have been some conspicuous bravery on Hephaestion's part in this action, and this is why he gains a special mention.