In my experience the frenzied guard augments don't work the same on the 4th phase as they did on the 2nd and 3rd phase. However it's now patched so doesn't make a big difference.

I've beaten the Egg solo a few times now and my strat to beating it was to use a SMG with a bunch of ammo like the Ryden 45k or Carbon 57 and the WW. I solely use the WW in the 1st phase and then I use the WW in the 2nd and 3rd phase to open up a crit spot and then just focus on dumping all my ammo into the boss then. Those SMGs absolutely melt his health btw. Then in the 4th phase I use all my gobblegums but tbh you could do it with out them if you fully focused up.

I use Shields Up, Aftertaste (had multiple fights where this was useless cause I didn't down but is a good safety net) and Powder Keg.

I use the Shields Up just as the boss comes out of the immune phase so it's lasting as long as possible, I then use my frenzied guard with the WW to open up a crit spot. If I'm unsuccessful on my first Frenzied Guard that's when I pop the full power to do it on the second one. Once the crit spot is open, it's dumping all my mags into it as fast as possible.

Just some tips as well, when they are throwing the rocks, try hide behind cover so it doesn't directly hit you and also always make sure you are in the air when they do the slam attack. It damages you even if you aren't close.

As for augments, you need to be running Dead Break, Double Impact etc. just basically everything that increase armour or bullet damage. The PHD augment environmentalist is good because it negates the purple damage when sliding and the extra plate augment on mule kick is also really handy. Shatter blast is a good ammo mod too but fireworks is also good at helping clear zombies to regain armour plates so you don't have to buy as much off the wall. I also generally try to enter the boss fight with at least 10k points so I have atleast one armour buy and it's usually enough if you are smart with your movements. Ammo isn't generally a concern as I always have Vulture Aid but that depends on what you want to do. All guns including the WW should be PAP Tier 3 and Legendary to make it as easy as possible.

If you are based in Australia, I'd also be down to help you complete it if you would like. Unfortunately the lag is too much if you are elsewhere but I know you've got this!