As with the base set, the Hardcore expansion had a 1st edition printing. The cards can be distinguished by a foil stamp in the lower left corner. Packaging including booster packs and boxes will also be marked, but they are very small and can escape notice.
The Hardcore set is rare in either edition, but appears to be exceptionally so for the non-1st edition. This may be due to WOTC deciding to end the printing early and discontinuing the game. We did recently confirm that there were booster boxes printed of the non-1st edition. Prior to that confirmation we had only seen blister hanger packs of 1 or 3 boosters.