1. Make sure your router is indeed in need of an emergency recovery firmware restore. On the ASUS unit I have, this is indicated by a slowly flashing power light and a clear lack of Internet connectivity. Make sure the other usual methods - power off, hold down the reset button, hold down the reset button as you power on, etc. - don't fix things.
2. Find a way to get a known good ASUS firmware image file onto your system. This is probably a file that ends in ".trx" such as "RT-AC66U_3.0.0.4_270.trx".
3. Unplug all other network devices from the unit, and connect your Mac or other system to the ASUS unit with an Ethernet cable plugged in to port #1 on the router.
4. Setup your network configuration so that you have a static IP address on the 192.168.1.0/24 network block. I used 192.168.1.10 with a netmask of 255.255.255.0 and a gateway of 192.168.1.0.
5. Open a Terminal window and make sure you can ping 192.168.1.1., the probably IP address of the ASUS router. If you can't ping the router, the rest of these steps probably won't work.
6. CD into the directory where the firmware image ending in .trx exists (see step #2 above).
7. Run these commands from the terminal prompt, using the correct firmware image filename in the "put" command:
$ tftp
tftp> connect
(to) 192.168.1.1
tftp> binary
tftp> put RT-AC66U_3.0.0.4_266.trx
Sent 22765568 bytes in 76.5 seconds
tftp> quit
8. Give the router about 5 minutes to process the firmware image you've just sent it. I had to then manually turn the unit off and back on to get it to reboot into a working state. Once it came back up, I could again ping it and I could again access the admin GUI via the web.