In the past few years, we have covered plenty of geeky iPhone cases, speakers, and other accessories here. The Batmobile Tumbler II Case for iPhone 8 Plus is also worth a look. It holds your iPhone and can project the bat signal on your wall. It comes with a front LED lamp and rear lights, anti-vibration wheels, and a convenient projection switch.
For the light effect, you are going to need 3 x LR44 batteries. You can get yours for under $85 at this time. More info is available here.