The first 2 bosses (Jonny & Clevon) can be killed by 1 bullet by almost every player so if one of those are up chances are you haven't hit it.
So you are left with 2 bosses to remember if you've hit or not. Each boss is numbered so really you only have to remember 2 numbers for 20-30 minutes.
Most phones & (pads/tablets) have a app you can make notes on if you are unable to remember numbers. I know this is quite the pain but logging in every 20 minutes all day/night long isn't?