While listening to this great track, I couldn't quite remember what GRIMES song he's based "Heartache" on:
It took Googling "GRIMES swinging a sword in the desert", but I found it: The original is called "Genesis":
Jump to 1:10 in the video for the core of the song.
Also came across this: An excellent 8-bit rendition of Genesis. I don't usually go for chiptunes, but this is unlike most chiptune tracks that lean too heavily on midi or that ear-piercing Gameboy-reverb. Check it out:
Other versions are availble on the artists Bandcamp:
Update: More covers that aren't covers of Grimes - Genesis: Trevorsomething - Sega-Genesis. :)