This is going to be a grind, no way around it unless a trick is found. If so, I will update.
You gain bloodlust levels by getting kills and completing story missions. However, you don't get a lot. By the time I finished story mode and got the 1,000 kills achievement in Murder Marathon I was only at level 71.
The best way to level up is playing Murder Marathon. Every 14 kills will raise you up a level so it really doesn't take forever but it is going to be so boring and mind numbing. Good luck!