repairing a 2 inch square 'hole' in plaster

The easiest way to fill this hole is with a foam gun. Simply squirt the foam in the hole and allow to cure. Once cured,cut off the excess until flush with plaster. Then push the cured foam in slightly with your fingers to allow the hole to be filled. Be careful not to loosen the foam when you do this.. Next step is to fill the hole with any type of plaster eg. Finish,bonding dri wall etc. and allow to set. (Not cement) Make sure backing coat is not proud of existing plaster. Don't worry if it is you can scrape it back once it has set. Finally apply finish coat or easi fill to complete the job. Allow to set and dry out,sand if necessary once dried .

If the hole is deep and there's not a wide area you can get some strong cardboard and put it in the hole. Then get normal wall filler, fill it, let it dry and fill again until flush

If the hole is in a plasterboarded wall then the square can be cut neater using a multi tool (or even a sharp stanley) and a baton can be screwed into this to affix a new piece of plasterboard into the hole that can then be filled or plastered smooth to the existing wall. If the hole is in a wall that is back to Masonry or Brick then it can be PVA'd to control the suction, filled using bonding or hardwall, and then skimmed to be flush with the existing wall. This is a simple job for a plasterer but could also be completed by a decent decorator, handyman or willing DIY'er.

You definitely do not need to plaster the complete wall ,and i am not a big fan of the foam theory either ,us plasterers use the batten method its a very sound sold repair and when decorated never no there was a hole there before .