VB makes a good point about stress, but personally I think its more upside down : bad diets make you susceptible to stress. I linked to http://thelovevitamin.com because she controls her skin with diet (just to point out that it is possible), but I don't agree with her diet, as some things she eats (like lentils and nuts) cause big problems for me, and I think the only reason she tolerates them is because she does so many lifestyle changes like yoga classes (things I don't have time nor interest for).
Paleo without nuts pretty much reduced my acne to 2-3 small zits, which was kinda okay, way better than it had ever been. Whenever I had an exam, presentation, date, ... I would get a big zit. I wouldn't be able to cope with the stress, even if it was low. So Peat kinda interested me for this.
Right now my sleep is just perfect, I never wake up at night anymore and can finally sleep in a room with light shining in it (and I need less sleep). Last time I had a presentation I didn't get any skin issues, and felt quite okay. I wasn't even very stressed out for it, and managed to improvize during the whole thing which is quite amazing given the fact that I used to be mister ultra-shy-boy.
Some interesting stuff that I found out is that I just get acne on my chin if I don't eat enough sugar. Eating lots of dairy and fruits do not trigger acne when I eat liver and oysters regularly, and I found out I can replace liver and oysters with retinol and not get acne. The biggest change you gotta make is reduce PUFA intake to an absolute minimum though. Some things like coconut oil and butter have PUFA but their saturated fats are protective. But nuts, fatty fish, olive oil should be avoided. If you decide to supplement vitamin A, you can use Nutrisorb-A on your skin itself, it's water-soluble vitamin A. Doses are personal, I've heard of two people that need 70.000iu to get rid of acne, while I personally need around 25.000iu depending on how much milk I use. Cliff also got rid of his acne and he apparently needs 50.000iu.
Ray Peat said that usually, when people supplement thyroid hormone and eat liver, their acne clears up. I can vouch for that, but I think PUFA elimination should be done too.
There is so much to be talked about, but I'm gonna stop here. I'd say give it a try, you can always go back to your old diet if it doesn't work.
EDIT : just wanted to add that a Peatarian diet also enabled me to cut out lots of supplements (magnesium citrate, vitamin C, B-complex, selenium) that initially took care of some of the acne. I still take B3, fat-solubles and eggshell calcium, but I'm slowly transitioning to only topical supplements (the retinol works quite well on the skin for example).