Here is a way to gain instant credibility with your boss: Tell her about a mistake that reflects poorly on you.
People's instinct is so often to hide or soften this kind of thing, but in fact the more blunt you are, the better you will come across. Just say it: "I really screwed something up." "I was completely wrong about this." Explain what you did, why you were wrong, and what you propose doing about it now. This also works in retrospect. Tell your boss, "Do you remember how last month I argued for moving forward with that project when Bob insisted it was a bad idea? I was wrong. Here's what I've realized since then."
Not only is this incredibly refreshing, but it's powerful because it instills in your boss the confidence that you will give her bad news directly -- she doesn't need to worry that she'll only get negative information if she digs for it. It also tells her that you have integrity and that your priority is to be honest and objective, not to protect yourself. And if you're ever in a he-said/she-said situation with someone, the person more likely to be believed is the person who has a reputation for being scrupulously open even when doing so won't reflect well on them.
Disclaimer: If you are confessing a mistake every week, this will not work well for you. This only works when you're competent overall but making the occasional normal human error. (Although, frankly, if you're incompetent, you're probably better off being up front about mistakes and asking for help than hiding them. But I do not have incompetent readers.)