The instakill moves (I don't remember what they're called in GG but they use the whole Tension bar etc etc) require you to hit four keys at once to activate Glowy Red Mode (again, I'm FAIRLY sure that's not the correct term for it). Once you're in Glowy Red Mode you quarter-circle-forward twice and then HS to perform your instakill.

The problem? I can't seem to get Glowy Red Mode to work, probably because pressing four keys at once on a keyboard does nothing until you release them, at which point only three are sent to the computer. Anyone have any suggestions to overcome this issue?

It's super cool to see GG X2 #Reload on GoG, it's my favorite fighting game of all time.

To overcome this, go to options, then controls. There you'll see you can map a single key to be "K + P + S + HS" which when pressed makes go into insta-kill mode (glowy red mode). After that you should be able to perform an insta-kill easily.

What Jotamide said.

Also, you should bare in mind that the game only comes with four face buttons and two shoulder ones preset, so you would do good to open the config executable, if you haven't already (you can find it in the same folder as the game exe, or in Start > All Programs > GOG.com > Guilty Gear X2 Reload) and assign all the buttons you can, in order to have one free to map as K + P + S + HS, as all the preset buttons are already in use: the four face buttons are the aforementioned K, P, S and HS, and the only two triggers are assigned to Dust and Respect.

You should open the config menu nevertheless, especially if you're like me and grew up playing fighting games on the PC (One Must Fall: 2097 comes to mind) and got used to move the character with your right hand instead of the left one (if you're an old-school PC fighting game player, you'll probably won't feel comfortable with WASD controls, rather preferring a control scheme more like "IJKL" and having the face and shoulder buttons mapped to QWASDZXC, for instance).