The reality is that none of us will put forth much, if any, sustainable effort to achieve something in which we don't believe. Another saying related to this is: "Where there's a will, there's a way." Meaning that if we want something bad enough (and "wanting" is a form of belief), then we will find a way to achieve what it is we want. Like with any maxim (or "rule") there are always exceptions. But the fact is that one will achieve far more by "believing in" what they want to achieve than they will if they *don't* believe in what they want. It's common sense.
Yes, I believe that there is merit to the phrase, as you believe, so you will achieve, because a person who does not think that they can do something won't. Belief is the first step in taking action to make something happen. A person who believes is more likely to put the plan into action.
Many authors have been quoted for similar statements as, "As you believe, so you can achieve." Research of the most successful people in the world has shown that their success begins with a strong belief in their ability to success in their chosen field. Anyone who believes they cannot do a certain thing will surely fail before they've even begun.
No, simply believing doesn't do anything for anyone. To get anywhere, to obtain anything, in this country, you have to work hard to do so. You can't just believe you'll get somewhere or get some material thing. It takes hard work and dedication, especially in the United States of America. That's who we are.
Growing up in the 80's and the 90's it seemed the world tried to tell me I could grow up to be anything I wanted to be. As a 30 year old, I realize that big bucket of lies for what it was. The quote, "as you believe, so will you achieve," reminds me of these lies.