There are lots of cases where the first piece is an adjective (even a participle) or an adverb instead of a noun, but battle-hardened is not one of those. Therefore it really must be a typo, because it means hardened by battle.
Most of the compounds where the second piece is a past participle and the first piece a noun work that way. For example:
air-cooled, belt-driven, carbon-dated, deer-proofed, feather-topped,
hand-sewn, gas-powered, iron-plated, jet-propelled, knife-edged,
love-begotten, market-tested, need-rooted, oil-tempered, punch-drunk,
quarter-sawed, rain-proofed, store-boughten, tailor-made, user-oriented,
vacuum-packed, wind-swept, X-linked, yeast-bitten, and zero-padded.
Those all mean “verbed by/with/for (the/a) noun”.
There are also many versions where the first part is a noun but the second part is now a present participle instead of a past participle. These mean “verbing (the/a) noun”. For example:
air-breathing, body-snatching, class-leading, death-defying,
deep-searching, earth-moving, fact-finding, gas-guzzling, hair-splitting,
iron-binding, jaw-breaking, key-winding, king-killing, labour-saving,
market-leading, night-flowering, orange-fuming, penny-pinching,
rabble-rousing, sabre-rattling, thought-provoking, underside-couching,
water-bearing, and yuck-making.
However, there are some that admit both versions, like fork-tailed and forked-tailed, so it is not a bad question that you have asked.
There do exist other examples where both halves are in participle form besides just forked-tailed, but these occur at about three orders of magnitude less frequency than the first set. Other examples like that are words such as broken-hearted and cloven-hoofed.
Those work more like big-hearted, deep-rooted, half-baked, etc., because the first word is no longer a noun but a modifier, either an adjective or an adverb.
Appending the text of Janus’s insightful comment so that its text not be lost, and be searchable:
Words like broken-hearted also have in common that the second member of the compound is a noun, rather than a verb, to which has simply been added an adjectival suffix -ed. They’re not real past participles. You can (just about) consider to battle-harden or to wind-sweep a verb, but there is no such verb as to forked-tail or to broken-heart.