Just like it sounds, you must land the killing blow to an enemy Titan on foot with your own weaponry instead of BT. This is not as insane as it sounds. At any point in the game where you find yourself down to a 1 on 1 with a titan, try to chip their health down as low as possible with either the starting loadout or the Tone core. Then while they are hopefully stunned from your last shot, disembark and unload on them. A shotgun or grenades are your best bet from close range. If you die but it's still destroyed, it still counts.
I cannot confirm or not if a rodeo kill counts for this