The only effective way to lose fat, and virtually pure fat, quickly is via Alternate Day Fasting due to the huge spike in growth hormone which mobilizes fat for energy in the short term and protects muscle. Up to 90% of the weight you lose will be fat, far above any other method which at best is 50% fat, 50% muscle.
I've dropped 8-10 lbs a week at the start and 4-5 lbs on a continual basis is good depending on how much you have to lose. I also had a no holds bar cheat day once a week to boost leptin levels back up and ended up down 35 lbs in 9 weeks, and that included only losing about 4 lbs the last 2.5 weeks...
Other than that you basically have to be happy with losing muscle at the same time due to the hormonal environment your body is in...
Best advice either way is lift heavy to preserve as much muscle as possible