Since it is not a real difficult halftone, I would make a single row with a blend of shapes, and then paste it as tile in the shape.
Off course I used Freehand, less steps, but it would be similar in Illustrator
Make the pattern
- draw 2 circles small and big at the beginning and the end
- create blend and set the right number of steps
- draw transparant rectangle behind it
- group blend and rectangle
- copy to clipboard
Fill the shape
- make bounding shape
- clone it
- select back one
- apply gradient fill
- select front one
- paste tile as fill
1 minute work.

I don't put the gradient in the rectangle of step 1 as that gives a risk of vertical white lines appearing in the gradient.