A lot of high school courses will require you to take biology as a prerequisite to psychology. However, I don't think biology is THAT important. Neuroscience, a very deep branch of biology, is essential when it comes to psychology. However, most of what you learn in psychology does not require biology.
I'm not sure if you are a college student or in high school still. I'm a Psychology major, and I understand where you're coming from. Both Math & Science are the hardest subjects for me. It's especially difficult when the two often go hand in hand; a lot of science requires you to do a certain degree of math. Honestly, in terms of your transcript, most universities will weigh their decisions based on your overall GPA, letters of recommendation, essay (if required) & your SAT scores. Especially, scores from the SAT or whatever standardized test your school gives to its students.
In college, just as general education requirements, you will have to take at the very least- 2 math courses & 2 science courses.... No matter what you are majoring in. Biology is important. Especially, in terms of brain chemistry & functioning. The neurological aspects will likely be most important in regards to psychology depending on what field you plan to work in after graduating from school. There are many different branches. Usually if you work toward a BA vs. a BS in Psychology, less science & math will be required. Science based courses are the most important for those who plan to go into any of the research based fields or those who want to administer any type of neurological testing. Also anything medical like Psychiatry. If you plan to be a "talk therapist" psychologist in that field - science in the big picture - is good to have some background knowledge in, but isn't really going to be necessary in sessions with your clients.