Man, there is virtually no way you can beat BB with this. Take a look below, this is what you are going to face on Normal(first screen is general stats of BB, then each weapon individually):
Once, by accident, I jumped into Normal BB with my second mech:
I managed to kill BB, but I was left on a scratch, like 150 HP, and I won only because the final turn I overheated him on the shutdown!
The most feared BB weapon is the physical top weapon (Orb cannon), it hits for nearly 300 HP. So you are barely 2-shot for it. You will not survive more than 2 rounds…Upgrade the HP pool to 1000-1200 at the monimum, then find some weapons hitting 200-250. In other words, your mech has to be at least legendary, and maxxed legend torso.