As mentioned, in addition to draining the exhaust, you are trying to get the water out of those small metal tubes in the intercooler which is a vulnerable low point in the system.
Similar to blowing the water out of anything else, you need a goodly volume of air going through there at full pressure.
I use 100+ PSI air with a short, 5/8" hose connected directly to the air compressor tank with a ball valve that can be opened (not through a regulator or long small dia. hose). Connect the air and open the valve and let it blow until the tank is depleted down to 30 PSI or so. I close the valve and let the compressor catch back up to full pressure in the tank. That also lets any remaining water collect back into one place in the low spots. Then I open the valve for a second burst of full pressure air which will push any collected water through the low spot. After three cycles of that, I don't hear any water bubbling inside, so it seems to to get the water blown out.