You only have to do one section and duplicate it but you do have to do the first strip.

And if you find that its looking to angular when you smooth it make the holes square by removing all centre edge loops.

OK you can do it that way for the main part but no idea how you would do it for the top.
Your image seems to have way too many holes, compared to ref.

Here is how I would do it from were I just...

To start off with the basic shape I would do this

1) Start with sphere (mine in pic is 12x12)
2) Delete lower part
3) Extrude the lower edge
4) Repeat untill its enough
5) Scale it up and...