Sigh. Just as well, I suppose, I got the coordinates wrong anyway.
The archon grimly hustles to 35N110E25Z (this should put him directly above the center of the darkness; correct the coordinates if it doesn't.)
The following round, the archon moves (if neccessary) over the center of the darkness, then fires a bolt straight down at the center (if no move was needed do a full attack). Repeat (double-moving as needed), until the cat is dead, or the archon misses too many times.