I was trying to do this route, but without using autofire:

I missed the fast platform cycle, but I got excellent RNG on the boss and a 2-cycle.

The boss 2-cycle is hard. The main thing to note is that the boss seems to have a huge hitbox, so you want to start stabbing pretty early as it comes down. At the time, I had a theory that the the boss took damage per frame of sword contact, rather than one point of damage per sword hit. So my strategy was just to mash to maximize "damage frames" and hope for the best. After reviewing footage of various runs though, I don't think this is actually true, and it might be more consistent to try to time your initial swing correctly.

The pre-necklace section in this run is slow. Partly because I got bad luck with bats but there are also some intentional slow strats that are required for the fast platform cycle:

• I break the wall at 0:10, which makes getting to the necklace slower, but allows for a faster return trip. If you are going for the slow platform cycle, it's faster to break it on the return trip (you don't lose time since you need to wait for the platforms anyways).
• I pause slightly before collecting the necklace at 1:24 to time a jump into the slime drop. Since the platform cycle starts when you get the necklace, you want to minimize the time between getting the necklace and doing the first deathwarp.

This other run I did has a better pre-necklace segment but slower time overall.

The slime jump strat at 1:15 is suboptimal. It's faster to stab the slime but I'm very inconsistent at it. See 1:15 in this run by Squarshies for an example of stabbing the slime.