What does "work on my tan" mean?

Here is the context:

He

It's not gonna be easy

She

Well, I don't do easy. If I wanted that I'd move to Florida and work on my tan

Work on in this sense in the literal sense means that they are going to try and become more tan.

You could say: "I am going to work on my car" in this case, it would mean to fix/repair "I am going to work on my thesis" in this case, it would mean that they are working towards the completion of their thesis.

There is a lot going on in this. If you look at the entire text, I would say that the root meaning of the last sentence would just be a declaration/example of something that is easy to do(since tanning is simply laying in the sun).