Oyez, oyez! Hear the news!
I beat Death (the eyes and evil torches boss at the end of the Apocalypse Trail), but only by cheating. As I said above, I have reliable strategies for the first three rooms and a passable one for the fourth. I now have a reliable strategy for the last room, too, but I had to use the save-while-glowing feature of god mode to get a chance to develop one.
Strategies:
Remember that fireball timing and aiming is slightly random. These paths are highly effective ways to get through the rooms, but you'll still die a bunch.
0. Drop off the ledge and fall in the middle of the gap.
1. As soon as you reach the middle, start moving left again. Don't stop holding left until you clear the room. Jump a little after you hit the ground; the aim is to jump from about an eye-width in front of the eye on the ground to a little beyond it. This will cause all the fireballs to go too high. Climb the left wall as fast as you can; you should just make it past the flying robot.
2. Drop to the middle of the space in front of you and wait until the eyes are close to firing. Double jump up to the right wall, then jump over the fireballs and run left, jumping over the laser. Pause just to the left of the laser for a moment, then run left to the next laser and jump over; you should easily dodge all the fireballs and the sweeping laser. The jump is very, very high, right at the limit of Juni's ability, and was the cause of a huge number of deaths before my previous comment.
3. Wait a bit on the lefthand wall, then drop (don't jump) and air jump just high enough to dodge the spike beast. Jump over the second one and run out of the room.
4. Move right a little, then get up the lefthand wall as fast as you can. Double jump right and try to jump over or run under the spray. I have terrible timing so this isn't something I can help with much.
5. This room features many of the red-eyed tentacle-women that appear only when you face them. Run right and turn to face left for a moment, the repeat; double jump to clear the fireballs. Repeat this, but be aware that the time to jump to avoid the second set is slightly sooner. Do not jump for any reason other than to avoid the projectiles. After this it's just a matter of dodging the alternating lasers protecting the clock (sides, then top and bottom); don't try to reach it as you fall from your jump.
I went to the moon and got as far as the tower to the stars, but decided against going up (as there's no way back). You see, one of the scientists in the museum said that it's possible to beat the Apocalypse Trail without the hologram...
It's surprisingly easy, by which I mean "HOLY COW, when did I get this good at KS?" I breezed through Pestilence and half of War. (Still can't make progress in Dark Sea II.) I'll update you all if I get further (because you're on the edges of your seats, I'm sure). Anyone willing to take on the challenge?
In news of interest to people who don't enjoy Lunatic difficulty, this level inspired me to write a story about Juni. (Aaagh, the plot bunnies, how they plague me!) It's mostly finished, but I've been stuck on the last bit for months. I'll put it in the Development Showcase board when it's done.