The relevant sections of the Crowland Chronicle, a long-running history or chronicle from Crowland Abbey, certainly do not love Richard. This is typically considered one of the more important sources for his reign, but (of course) problematic. The text, true to its genre, unites externally-verifiable facts with hearsay and fama. But it definitely has an opinion on Richard. He's "crafty", "haughty," he "wastes" the money and treasures his brother had carefully amassed to satisfy his pride. He's duplicitous:

The duke of Gloucester, however, who was the ringleader in this outbreak, did not omit or refuse to pay every mark of respect to the king, his nephew, in the way of uncovering the head, bending the knee, or other posture of the body required in a subject.

Definitely a usurper:

The colour for this act of usurpation, and his thus taking possession of the throne was the following: It was set forth, by way of prayer, in an address in a certain roll of parchment

He deserts God and God deserts him:

It was fully seen how vain are the thoughts of a man who desires to establish his interests without the aid of God...At day-break on the Monday following there were no chaplains present to perform Divine service on behalf of king Richard...During the night he had seen dreadful visions, and had imagined himself surrounded by a multitude of demons

He deserts his wife on her deathbed...for a reason:

The king’s purpose and intention of contracting a marriage with his niece Elizabeth being mentioned to some who were opposed thereto, the king was obliged, having called a council together, to excuse himself with many words and to assert that such a thing had never once entered his mind. There were some persons, however, present at that same council, who very well knew the contrary.

The chronicler goes to some lengths to show, again and again, how the people of London and all England turned against him:

A certain poet composed these lines:

(Richards I and II)

Edward’s vast hoards of wealth consum’d, the Third

Was not content therewith, but must destroy

His brother’s progeny, and then proscribe

Their partisans. Two years had he usurp’d

The throne, when, meeting these, he lost his life

And ill-gain’d crown, upon the battle-field.

...although one must note, this "certain poet's" comments on Richard align directly with the previous comments of the chronicler.

And finally, the Crowland Chronicle gives us the famous line:

As it was never heard...that any other persons, after the termination of the warfare, were visited with similar punishments, but that, on the contrary, the new prince had shewn clemency to all, he began to receive the praises of all, as though he had been an angel sent down from heaven...

Again, the chronicler takes pains to show it's fama--common sentiment--that Henry is an avenging angel. But the emphasis on fama decreases the, shall we say, objective credibility of the work to some extent. Where the work tries to attribute motives to Richard's actions, or implicate him in conspiracies at different points, it's not presenting evidence: it's presenting after-the-fact reputation (above all in the chronicler's own opinion).

I do think it's well worth revisiting the source material on medieval figures that we've inherited a biased view of. Rereading inquisitorial reports, chronicles, letters, laws, and basically the entire medieval European corpus through critical eyes, instead of accepting everything at face value as Actually Happened or Good Judgment, has revolutionized our understanding of--for example--FIFTY PERCENT OF MEDIEVAL EUROPEANS. (That is, women).

But the goal of a critical reassessment is better understanding of the Middle Ages. When we see powerful medieval women stomping on each other to hold onto their positions, reinforcing the "weak women/transcending her sex" trope, or just being average women living their lives in a sexist society, we have to accept that as much as we work to show how women writers worked with and against their social constraints to produce amazing (and decidedly un-amazing) literature.

Whether or not this process means a rehabilitation of Richard III, or rather to what extent he can be rehabilitated from Shakespeare, is a matter of how you choose to interpret the sources.