From the beginning, get in the scorpion and proceed through the level as normal until you reach the "Kizingo Boulevard" gate and checkpoint. When you enter this area, you should hear a marine say "I gotta take the shot!", which means you are in the correct area.
1 - Get out of your scorpion and kill on the marines riding on the side
2 - Clear ground enemies, wraiths, ghosts and dropships, but be careful to keep the banshee up
3 - Circle around the roundabout and you'll find a back alley. Park your scorpion halfway up this alley.
4 - Lure the banshee into this alley by trying to make it follow you. It must get caught trying to turn around.
5 - If lured correctly, it'll faceplant!
6 - Go behind the banshee and shoot the pilot using the SMG or a Beam Rifle. DO NOT melee them! As you are shooting them, it is CRITICAL that you hold the "board" button, which is
7 - If you successfully kill the pilot while holding the board button and without blowing up the banshee, you will automatically board it as they die.