a) Tyrrell's soliloquy highlights the themes of good versus evil, ambition, and the corrupting influence of power. The monologue marks a turning point in the story. In having the young princes murdered, Richard has stepped beyond the bounds of decency and has sealed his impending doom. Through Tyrrell's speech, Shakespeare lets us know that Richard's eventual defeat at the hands of Richmond is assured. No monarch can continue his kingly reign after such atrocious murders, and, although he is physically deformed, Richard will not be exempted from judgment.
Up until the murders of the princes, King Richard had targeted adults. However, Shakespeare understood his audience's religious and societal sensibilities: the murders of innocent children would never be tolerated. Strong repercussions against the murderer(s) would be expected. Shakespeare does not disappoint, of course.
On the night before the battle, Richard is beset by the ghosts of his victims in a frightening dream. It is a terrible omen, foreshadowing the wicked king's death the next day. Accordingly, the soliloquy is significant because it marks a turning point in the story and foreshadows impending judgment to avenge "The most arch deed of piteous massacre/ That ever yet this land was guilty of."
b) The purpose of Tyrrell's speech is twofold. First, it confirms to the audience that the young princes (King Edward's two sons) are dead. Second, Tyrrell's soliloquy describes how the princes died and who carried out the assassinations. From the soliloquy, we learn that Tyrrell himself did not perform the murders; he hired two men, Dighton and Forrest, to accomplish the terrible task. The murderers, described as "fleshed villains" and "bloody dogs," were used to committing heinous acts against their fellow citizens.
However, both men found little joy in killing the young princes. They describe the children in angelic terms. The princes supposedly had "alabaster innocent arms" and they were God-fearing children: a book of prayers lay on their pillow as they slept. After committing the heinous acts for which they were paid, the murderers lamented that they had "smotherèd/ The most replenishèd sweet work of nature." By reinforcing the murderers' remorse, Tyrrell's speech highlights the contemptible nature of the murders. Although hardened assassins, Dighton and Forrest felt no joy in killing two innocent children.
In fact, both refused to speak to King Richard about what they had done. Their behavior shows that they have not yet relinquished their humanity and that their conscience remains an intrinsic part of who they are.