Will getting good scores on the SAT and ACT boost the chance of getting into top tier universities?

I was really set on just taking the SAT, but I was advised to take both the SAT and ACT. I was thinking that I would focus more on the SAT when preparing for the SAT and ACT. What if I would do better on the ACT than the SAT? If I did well on both, would universities be more likely to accept me?

There is no point in taking both. Do well on one, and you’re done.
Most universities will only care about your top score, and NO university will be more likely to accept you if you took two… the person who advised you to take both either does not know what they are talking about, or they really meant for you to try out a practice test for both to see which test suits you better.

If you score low on the SAT you can try the ACT. If you score high on the SAT forget the ACT.

^ Yes.

Not getting a good score on one or the other of these tests will hurt your chances of getting into top universities. They will have many, many qualified applicants who have extremely high scores on either the ACT or SAT or both. Everyone is different - some people are better at the ACT, some better at the SAT. Try taking some practice tests on both and get a feel for which one you are more comfortable with, focus on that one, and go from there.