As someone with high anxiety, I can relate. Everyone has their own methods for beating it, but here's mine when it comes to ss13.
Winning doesn't matter. You might hear it a lot already, but its true. Greentext doesn't matter, and nobody will care about it.
Think less, act more. Once you get into the groove of rampant violence (or stealthing your objective if that's your thing) things become a lot easier. Starting it is what makes your heart pound. Continuing it is what gives you the rhythm.
Even the "pros" get instantly tazed and gg'd sometimes. It happens. There is absolutely no shame in it. Not every situation is beatable either, so don't be hard on yourself for the destined failure.
I'd also recommend taking adrenals/freedoms for a while till ya get used to the roll of antag, so you aren't defeated with one lucky taze, but thats out of scope of your question.