If you are struggling with it, take it one wave at a time. Defend the blocks to the top left as best as you can. Kill almost all the zombies of each wave, leaving one or two alive. Shield bump them into a corner and hope they forget about you. Then, break the top right block in the wall of blocks that surround the Heal Pad, letting you slip in. The Zombies should get stuck on the blocks. Patiently wait for full health, before starting the next wave.

The first wave is the single Trojan that hits the ghost blocks. He will almost always either do a pulse or, very rarely do an overhead strike. I tend to charge up a Flourish or Blitz when I step on the button. Then, when the ghost blocks go down and you have slipped behind him, the Trojan should be just finishing his attack, giving you the opportunity to one-shot him. The Red Rovers are the easy part. The next wave is just tons of Zombies. If you have soloed your way up to that point, said Zombies shouldn't be a problem (Don't forget to heal in between waves).

With the third wave I try to do one of two things: 1) I try to rush the Trojan, hoping I can one-shot him with a Blitz Charge before zombies come in. I do not suggest this, because you will probably get interrupted and trapped real easily by zombies. The better option is to use a Pulsar or Brandish/DA charges while camping on the left. There should be only about 3 zombies spawning on the left side of the room, while there are about a dozen on the right side. When the fire goes down, move to a different section, and constantly whittle down the zombies. The Trojan will be chasing you, so make sure you keep an eye on him. When the Zombies are down to three or four, then you can take down the Trojan easily. Do not kill all the Zombies, for that will spawn the next wave, even if the Trojan is still alive (I have had runs with 3 Trojans at the end).

For the 4th and final wave, the right will have the least Zombies if I'm not mistaken. Try to get an AOE elemental attack off when the Zombies spawn and repeat the steps above that dealt with the 3rd wave. You will have to be really careful to watch both Trojans carefully. In general for both the 3rd and 4th wave, try to keep Zombies between you and the Trojans. When there are obstacles in the way, the Trojan will either do a pulse to scatter a few Zombies, or charge, bounce off the Zombies, and then do a normal attack that probably risks hitting you (but will be easy to dodge and scatter the Zombies again).

Oh, and killing the Zombies opens the gate, so you can technically make it to the elevator with 3 Trojans swiping at your ankles/head. If you can dodge Trojans for long enough, you can kill the Zombies, and then break the Heart Boxes behind the gate for full health before you take on the Trojans.

some small corrections to hijack the hijacker :D
for the third wave the mass of zombies spawns on the LEFT so camping on the right side would be preferable.

about smoldering steps:
-I suggest killing the trojan in the third wave BEFORE killing the last zombie of that wave, this can be achieved by shieldbumping the last zombie to a corner of the room and luring the trojan to the other. the difference between having 2 and 3 trojans is pretty huge especially when you're not that experienced yet.
-I personally find it harder to keep track of 12 zombies' movements. when i solo i take out the red rovers first. Getting stuck between the gate, a turret and the trojan will usually kill you though, so keep watching the trojan!

another alternative strategy for the gun puppy room:
1. kill first 3 zombies on the left
2. lure bottom 3 zombies to the left and kill them
3. kill the gun puppy once, if you're using a polaris you attacks should completely disrupt the puppy's attack. then quickly run to the right and continue your way slaying the last 6 zombies. the puppy can be let alone from then on. since it respawns facing down, it will not attack you again unless you attack it first. when travelling with an unexperienced group ask them (friendly) to stay outside since an attack on the puppy while you're busy fighting with the zombies can easily hurt you both badly or even kill you.

about charred court:
I personally like polaris alot here, if used appropriately. as i play with gun damage bonus maximum my polaris does not do less dps than a brandish
and you can line/clump up zombies for your mates to increase they voltedge/DA/combuster/glacius charge damage.
in the last room after 3 or 4 waves zombies willl start spawining in the spikes and are way harder to access with a sword unless you have someone with a electron vortex pulling them all together. Here, a polaris spamming knight at the bottom of the spikes helps hoarding up zombies as well.

to add one more advice: listen to experienced players who are trying to explain you what to do. they usually try to improve the run's quality by making you a better player :)

Best hybrid gear for FSC :3!!

Divine Avenger, Final Flourish, Blitz Needle and Valiance

DA for usual zombie stages, FF for zombie when you feel like attacking without charges, Blitz for vana and trojan, Valiance as a backup gun and the mask stage. If you are holding Shiver change the Final Flourish