it's necessary to upgrade your electrical, you might not need new battery, do the Big 3 and see if you still have problems, then get a second battery if dimming persists.
what is the big 3? i have a 12'' re se dv4 wired to 2 ohm with ap15001d. the amp will put out 950watt max here. but even with amp gain not even half way, if my volume is really loud my lights get dimmed.
edit: nvm figured out the big 3 lol. and im using 4 gauge wire