These two achievements revolve around completing a teleport event while under a certain amount of HP. This can be difficult to complete for several reasons. Mainly that you need to regulate your health so that it is low, but not zero. Cuz enemies are shooting at you. I managed to find a way to do these things within a dream. And yes, it was in a dream that I came up with this plan.

The first thing you need is a mod. Yes. If you want to do it mod free, you can. But for this we need a mod. And not a unlock-all-achievements mod. This little mod is called NoBossNoWait. A mod that is useful in it's own right. It makes it so once you kill all teleport bosses, the teleporter charges all the way. It saves a lot of time, and makes these challenges pretty easy. This mod is downloaded with R2modman. Here is the link:

https://thunderstore.io/package/mrchous/NoBossNoWait/

yeah if the link doesn't work literally copy paste it into google.

Next step is play as Rex. Because his skills use up HP and one of these achievements is literally for REX. The last step in this master plan is getting a Trophy Hunter's Tricorn.

I only now realize that it's a SOTV exclusive item so if you don't have the dlc you're kinda ♥♥♥♥♥♥ LMAO

Activate the teleporter event, use Rex skills until you at 10% health, and use the tricorn to immediately end the teleport event.

find the teleporter. Use rex skills to get to 50 HP or lower, or use shrine of blood, or a void cradle. activate the teleporte, make sure you stay under 50% hp, and use the tricorn. If you do these two achievements in the same run, you might need artifact of command to get two tricorns easily.