i'm assuming that the second photo is your hair now.
since your hair is already a bit lighter than your natural colour you're already part-way there.
to get to blonde you need to bleach your hair. end of. since you're worried about breakage it's better to do it slowly over time. the best thing you can do is bleach baths:
but you'll need to do them a lot and if you're doing them weekly then it'll probably still take up to several months.
alternatively, do a couple of regular bleachings. it's a bit more likely to give you issues with damage but it won't take as long. 2 or 3 bleachings with 20vol. developer will probably do it for you.
as far as dealing with the blonde hair, by the looks of things you straighten your hair through relaxing, using a straight-iron or chemical straightening. this is damaging, so you're more likely to get damage with the blond than caucasian hair.
so, if you do get blonde (yay!) then you can do a couple of things. firstly, get shampoo and conditioner for coloured hair, you can get some leave-in conditioners that are good and there are intense masks that you can get that you leave in for a few minutes and rinse (i've heard some great things about Aussie 3 minute miracle moist).
if you use a straight-iron then make sure you use a heat protection spray. if you can't afford one just mix some of your conditioner with water and put it into a spray bottle, works the same :)
i'm not too familiar with the products that are around for afro hair, but i'm sure there are leave-in moisturising cremes and conditioners, you should be able to find some in local drug stores or afro salons.
you can do a hot oil treatment as another moisturising thing for after bleaching (nice and cheap). heat up some olive, coconut or argan oil (or i guess any cooking oil would work) heat it in a bowl in the microwave and put it on your hair (don't burn yourself!) then wrap your hair in cling-film. leave it for 1/2 hour- 1 hour and then rinse it out.
i've heard something about home-made hair masks as well as protein treatments, but i don't really know anything about these.
hope this helps. if you have more questions then please ask away :D