Well, whether you dye it or let the sun do it's work, your hair is going to get damaged anyway. I'm not sure how much sun exposure it would take to get a drastic change in hair color; I think that would depend on your hair. However, I'd be more concerned about the damage the sun would do to my skin, especially since we're moving into summer.

If you decide to dye your hair, the method you described sounds rather reasonable. I know lots of people recommend bleaching dark hair in gradual steps to avoid lots of damage to hair instead of going from black to blond in one go, so I think the same would hold true for hair dye.

At any rate, just try to minimize the damage to your hair and treat it gently. Oh, and put on lots of sun block if you decide to let the sun lighten your hair for you. Good luck!

Any technique that lightens the hair will damage it.  Trying to lighten it more than 4 shades will require stripping the hair of its color which is one of the most harsh chemical processes you can do to your hair.

If you must "go blonde", I'd recommend having it done by a color specialist.  They should be able to advise you on what is reasonable to minimize the damage that will occur.