I'm also applying to a UCSB graduate studies program, and I'm currently writing my personal achievements essay too. I'm struggling to make my essay unique from my statement of purpose, while still maintaining an underlying 'this is why you should pick me' message.
With that being said, here is my two sense:
While I would not go into unnecessary, incredibly personal details about your life, I do think it's important to fully answer their prompt- which is basically asking you to share some aspect of your life that is personal, unique, and important to you. If your mental illness is an important aspect of your life, you could consider writing an essay framed in a way that shows how far you've come, how your education meant so much to you that you didn't let it drag you down, and how you overcame this obstacle.
If that is too daunting to write about, maybe you can write about your fellowship opportunity in a way that is personal to you. I wouldn't keep your essay as impersonal as possible, but rather highlight the important personal components with some explanation.
Also, while I think some overlap between your SOP and personal achievements essay is ok, I would avoid writing a very similar essay to your SOP. They are asking for two essays for a reason (I think/hope...) and they are not going to want to re-read what you've already written in your SOP.
Luckily for us, this prompt is vague in the sense that it asks us to write about virtually any aspect of our lives that is important to us (background, accomplishments...), something we want to share with them. It's a way for them to get to know us, and it's a way for us to stand out in the grad school apps.
