Richard III is indeed a villain. What's more, he positively revels in his villainy, and he makes absolutely no attempt whatsoever to disguise it. To see an example of this, we need look no further than the play's opening scene:
And therefore, since I cannot prove a lover
To entertain these fair well-spoken days, I am determined to prove a villain
And hate the idle pleasures of these days. (Act 1, Scene 1).
Richard has accepted the fact that, due to his physical deformity, he will never be renowned as a lover. So he's going to cultivate the reputation of a villain instead, a role for which his natural endowments suit him perfectly.
As this opening soliloquy makes clear there's no mystery about Richard; what you see is what you get. Right from the start, he's refreshingly honest about his villainy. At the same time, he doesn't completely take ownership of his wickedness. He implies that society has cast him in the role of villain due to his physical deformity, and that he's therefore only playing up to a part assigned for him by other people.
Further evidence of Richard's villainy, and his unwillingness to take full responsibility for it, comes in Act 1, Scene 2, where he tries to justify his murder of King Henry and young Edward:
Nay, do not pause; for I did kill King Henry—
But ’twas thy beauty that provoked me.
Nay, now dispatch; ’twas I that stabbed young Edward—
But ’twas thy heavenly face that set me on.
Here, Richard has the audacity to blame Anne Neville, the woman he's trying to woo, for his own killing of Henry, her late father-in-law, and Edward, her husband. He only killed them out of love for her, he claims, provoked as he was into committing these heinous acts by her beauty.