Compressing a gas to nearly 100x it’s natural density is going to dramatically increase it’s temperature. In simplified mechanics, you can basically think of it like all the energy that makes it the temperature it is naturally will still be there when it is 1% of it’s original size. So all that energy is “overlapping” and adding together to make it’s new temperature based on there being 100x as much energy in each place now. Even if it started at 10 degrees Kelvin, assuming a linear gain, it would be 1000 degrees Kelvin after compressing.
Of course all of that is super simplified and not the “real” math or mechanics in all their complexity. But it should help illustrate why it would not be possible or a good time.
And that is only the temperature half of it. Compressing an area to 100 atmospheres, which I’m presuming would be the level of pressure necessary to get that gas (or a safer slightly less dense one) to the needed density range, would also be pretty dangerous if not immediately fatal to the human. Again that level of pressure is assuming a linear gain, I don’t know for sure if it would be linear.
So even if you manage to find something you could breathe, you wouldn’t be able to at that level of pressure. You would need to be wearing a suit that can be pressurized and breathing from something that isn’t feeling that pressure. Which completely defeats the whole point of choosing a medium to be immersed in that doesn’t require a suit or tank like being in water does.
It is however, theoretically possible to breathe liquids. Just incredibly uncomfortable for humans. There are humans that have survived it in experiments. After an initial adjustment period where your brain is certain you are drowning for a few minutes, eventually you are able to over ride that when you don’t die. Then you can hang out for a bit not dying despite it seeming like you should be… and then when you are done breathing liquid, the terrible part starts, you have to get the remaining liquid out of your lungs so there is room to put air in them again. As much as the rest is not great, transitioning back to air was universally considered the worst part of the experiment.