If you havn't you should give the original Qix a play. It has a few more mechanics and its enemy, the Qix, is way cooler (and the audio is kinda crazy).
But in this remake and the original a good strategy is to build traps; Construct a tight narrow area close to an edge, and then bait the enemy into it. Once it in there, do a quick short path to seal the entrance to the trap and fill in 90% of the board really quickly.
Its a cool classic game.