I never really planned on uploading this, but since Freedom Planet 2 releases on consoles today, I thought that I might as well show it off. The rest of this description will explain the methods I used to consistently get through each phase for those of you who eventually try this, since I couldn't find a guide here myself.
Getting this out of the way: you must have the One Hit KO and any other brave stone of your choice equipped, as long as it has a 25% bonus, otherwise you will not pass the 200% bonus, and only get a regular S rank.
For those that didn't already know, Lilac can cancel her Dragon Boost by pressing the button for Dragon Boost again.
Blue Moon - This phase doesn't have too much to worry about. I like to deal as much damage as I can just to get it over with, but if you're taking a slower approach, you just have to be careful with the streams of water Merga will summon. Those things have a massive hitbox and I've lost some runs unnecessarily due to underestimating how far I'd have to go to be safe.
Blood Moon - This phase is probably the easiest and most consistent one. You can take a bar off of Merga when she rises, which will force her into summoning lava on the next attack. You can take another bar when she is about to summon the lava, as Lilac's Dragon Boost grants invulnerability until it ends, so you will be safe. You can take the third bar when she starts descending from that attack, and then the last one on the next attack with good positioning.
Super Moon - This phase is about as consistent as Blood Moon, since you can finish it before she gets a chance to limit your movement with the long swords(?). Take a bar when she rises, then another when she starts aiming the sword at you. This should make her use her blaster, which takes the sword off the screen. When she fires the blaster, go to the other side and then a properly timed Dragon Boost cancel will take another bar. You can then take the fourth bar when she starts summoning the knives, and then the last one when she starts aiming another sword at you. If you cannot take her out fast enough, that is okay. As long as you stay above her when she aims the swords at you, they should be at an angle that doesn't threaten you.
Eclipse - This phase is where things will slow down a bit. The best strategy I found was to just play it safe and stay in the corner, dodging everything Merga throws at you until she jumps or teleports to you, which you then Dragon Boost cancel to get damage in. Sometimes she will delay her attacks in the corner, so you should use cyclone after cancelling Dragon Boost. If she attacks early, it will not hit you, but if she doesn't immediately attack, you can guard on the way down to be safe.
Lilith - This phase is mostly the same thing as Eclipse, in that you just want to take your time. Whenever Merga starts guarding herself, use a Dragon Boost cancel to open her up (this is to avoid dying to flowers that start appearing around her shortly after, I seriously lost so many runs to that trying to rush in), and then attack her 3-4 times before backing away from her Dragon Boost. When she summons the whirlwind, count to 3 and then Dragon Boost towards Merga, which should destroy some of the flowers that would otherwise be blocking your way. If Merga summons spikes from the ground, jump over the first set, get 4-5 hits in, then avoid the last part of the attack before getting a few more hits in (and then backing away).
Merga - The final phase is easy to get nervous on and mess up, but it isn't that bad. Dragon Boost is your best friend here. For the first half of this phase, you just want to get Merga offscreen. This will usually get her to use the attack where she rushes at you with her energy blades, which you can Dragon Boost cancel through to get some good damage on her. If she uses Dragon Boost, the first one seems to always be 3 boosts (whereas she could otherwise do 5), so you would want to run to the other side of the map and try to jump around Merga on her third boost, before going to the other side of the map to repeat the process. Once Merga is at half health, she will summon a lot of knives, 3 at a time. This is easily one of, if not the hardest part of this whole thing. I don't really have any advice, since I can't really consistently get through this part just yet. All I can say is to try and stay calm, and to only use guard if you absolutely must, or Dragon Boost. After this attack, you can go back to the process that you were doing in the first half, but just be wary of random blades she could throw after your Dragon Boost. If Merga uses Dragon Boost again, try to do the same thing as last time, except forcing Merga out of the corner on her fourth boost and then back into the corner on her fifth as to avoid the smoke cloud(?) from her Dragon Boost from getting in your way later.
Hopefully this can help you guys get your ranks, as this was very annoying for me to figure all of this out on my own.