You must enable the Source console for this. Default for the console is F10, case it doesn't work go to the game's launch options on Steam and add "-console"

1. Start a server on any duel map (map duel_winter for example), and have your achievement partner join you.
2. Insert these commands on the console: "vs_duel_rounds 1" and "vs_duel_timelimit 1.0"

Now every duel is gonna last one second and one round only, so you and your opponent just keep pressing B and you'll never stop bowing, just wait around 15 minutes and the achievement will pop up after 100 duels :)
I didn't figure how to disable the map changes, so the map does change after a few duels and / or minutes, so keep an eye out if the game changes maps!