What wall anchors should I use to hang a frame on plastered breeze block?
That's a light enough object that standard hollow-wall anchors (plastic plugs) should work fine. They'll do the job whether or not you hit a portion of the breeze block behind the wallboard.

Carefully locate the mounting points on the wall.
Drill for your plugs--usually 1/4&quot; or 5/16&quot;. Note that hitting the block will severely dull your bit. You may want to use masonry bits for that part.
Insert the plugs and then insert appropriately sized screws.