Physical is probably the king element in SMTV Vengeance but Battle Sutra is limited without going to Godborn or NG plus. This is how you farm it even on NG.
First, you have to unlock Bethel Egypt area. Then you teleport to Odaiba to check on the partner spot. The spot I'm talking about is actually at the top of the highway area. Here you see me peek a bit and see if it spawns or not. If not, I teleport back and went to Nagatacho. For some reason, area 1 is treated as a different 'map' for it to refresh the spot. I chose Nagatacho for ease of menu-ing.
At around 01:30, I found the spot HOWEVER, you need to go a bit forward and check if your partner went for it or not. On your bottom left map wise, it actually overlap with the spot I am talking about. The spot is above where I'm standing.
After confirming its the spot I want, I went to Bethel Egypt Approach because I think its faster this way. It won't refresh because you actually are still in the same area technically.
After I arrive, savescum it until you got it. I use Pixie here because apparently her "Item Rate" in the datamining is 2, whatevet thats supposed to mean but to be honest, all navigator is fine considering you savescum it. Please correct me if I'm wrong about other navigators.
Apologies for using raw footage and not edited to make this video nicer but sadly I'm using PS5 and dont have a PC for editing.
Also there are a few more spots for Battle Sutra but this is imo the fastest one.