Muriatic acid can be applied with a brush, left on for a while then rinsed off with a hose spray. Repeat as necessary, and perhaps scrubbing with an "acid brush". The acid solution should do most of the work.
Wet down the area and bricks before applying the acid. Protect any plants, etc. by prewetting and/or covering. Try and keep it off the caulk, but that looks easier said than done so monitor the caulk after the job in case it needs redoing. Rinse everything well when done to dilute the acid.
But I strongly suggest that you must hire a professional. To avoid any harmful effect, let the professionals do it for you. You can hire Austral Cleaning too, I’ve been their client for almost a year and I have been experienced their quality work.
I hope it can help you somehow!