How is Christ depicted as a hero in "The Dream of the Rood?"

In The Dream of the Rood, Christ is not only depicted, but also proclaimed a hero. The best answer to your question is to be found in the explanation of lines thirty-nine through forty-two which (in the mondern-language translation) read:

The young hero stripped himself--he, God Almighty--

strong and stout-minded. He mounted high gallows, 40

bold before many, when he would loose mankind.

I shook when that Man clasped me. I dared, still, not bow to earth,

Line 39 says that the 'young hero' stripped himself. In other words, He was not stripped, but of his own volition went unclothed so that we would not have to stand naked before the throne of God. It also refers to the great emptying spoken of in Philipians 2:5 - 8:

5  Let this mind be in you, which was also in Christ Jesus:
6  Who, being in the form of God, thought it not robbery to be equal with God:
7  But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men:
8  And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross.

This great emptying, where Christ--God Almighty--empties Himself of his supremacy, His holiness, His very divinity, and takes upon Himself the likeness, humility, sinfulness, and humanity of mankind. He does this voluntarily. Theologians do not make light of Christ's physical sufferings, His beating, the way the onlookers plucked out His beard by the roots as He passed, the nails which pierced His hands or the spear His side, but many often assert that His first and greatest sacrifice of suffering was when He did empty Himself and voluntarily place Himself under obedience--even obedience to the cross.

In Line 40 the passage continues: Strong and stout-minded He mounted high gallows...What a marvelous image of confidence and control, Christ mounts the cross as a warrior mounts his steed; He is not coerced, or forced, but He goes willingly, even eagerly.

Line 41: bold before many, when He would loose mankind. He knew the result of His sacrifice, just as He knew the requirement for the sin-debt of mankind. He knew the price of freedom and had come to pay the cost of it.

In line 42, speaking as the cross he says: I shook when that man clasped me... Again, Christ takes hold of the cross, He was not bound to it, but bound the cross to Himself.

In all of these lines, the poem depicts a person who is in the process of deciding His own fate; fate is not decided for or pressed upon Him. Additionally, the language depicts His choices as confident and masterful, He 'mounts' the gallows, he 'clasped' the cross.

In one of the Wheel of Time books, one heroic character says, "When you go to the gallows, go with a coin for the hangman, a joke for the crowd and a smile on your face." I think this realistic depiction of Christ more than exemplifies this heroic mien.

The Dream of the Rood is one of the greatest Christian poems and the first to truly depict Christ as a conquering king outside of the scriptures themselves.

Modern-language translation of The Dream of the Rood

Where is Christ depicted as a warrior king in The Dream of the Rood?

There are many different modern-day English translations of The Dream of the Rood, and the one linked below, from Rutgers University's Old English Poetry Project, is a fairly typical example. In any case, irrespective of which translation is used, every one of them recounts the same events.

In relation to the question, there are two specific events that warrant our attention. The first concerns the description of Christ as a warrior. It's not surprising that Christ is so described, given that the warrior was so highly esteemed and honored in Anglo-Saxon culture. Christ's sacrifice on the cross is presented as the kind of noble act of heroism that Anglo-Saxon warriors would be expected to perform:

The young warrior stripped himself then—that was God Almighty—
strong and firm of purpose—he climbed up onto the high gallows,
magnificent in the sight of many. Then he wished to redeem mankind.

Later on in the same stanza, Christ is further described as a “mighty king” heaved up above the ground by the rood. The depiction of Christ as an Anglo-Saxon warrior king illustrates how deeply this culture had incorporated the crucifixion of Christ into its own practices.

As with any great warrior king, Christ is utterly fearless, especially when it comes to death. Evidence of this is provided in the fifth stanza, where we are told by the rood that the Lord of Mankind—Christ himself—willingly hastened upon the cross, the very site of his death, with much courage.