Will dual enrollment make up for a lack of AP's?

My high school (a STEM-themed magnet school) doesn't offer any AP classes. Instead, they have duel enrollment classes at the local CC (they have them at the nearby state school as well, but I can't afford them). I'm only a sophomore now, but during junior and senior year I'll probably be taking almost all my courses there.

I'm not too worried about getting college credits, but will this hurt my chances at attending a top-tier school? If it does, I might try to take some APs at another high school, but I'm not sure how that can be done.

Yes, dual enrollment can be a good alternative to taking APs, particularly if your school doesn't offer AP classes. Because APs are more standardized than community college courses, it's possible that highly competitive top tier private colleges will prefer APs to community college courses; however, if your school doesn't offer any APs, then dual enrollment in community college classes is another viable option for demonstrating your interest in an academically rigorous schedule.

If you're concerned that colleges won't place as high a value on your community college courses, you can also try to take an AP exam at the end of a corresponding community college course. For instance, if you take a community-college level course in biology, you could take the AP Bio exam afterwards to demonstrate that the course you took was equal in difficulty to an AP course.

Finally, if the main barrier to taking classes at a nearby state school (rather than a community college) is the cost of the courses, it's also worth looking into financial aid and scholarships that you can apply for.