Note you're looking for a word that simply doesn't exist ("härtestens").
Some adjectives have forms that describe the absolute superlative of the adjective - without actually being the superlative (not comparing to something specific, but just pointing out the utmost possible extent), but rather an elative form (My take is that English calls this the absolute superlative as well). Your example is the adverbial usage of the elative.
schnell - schneller - am schnellsten vs. schnellstens
dringend - dringender - am dringendsten vs. dringendst
gut - besser - am besten vs. bestens
spät - später - am spätesten vs. spätestens
This elative form does only exist for some selected adjectives, for "hart" as in your example the elative form simply does not exist.
For adjectives that don't have a commonly used elative form, the elative must be paraphrased - "aufs Härteste", "in härtester Form/auf härteste Weise", "härtestmöglich" or simply "so hart wie möglich" might be amongst suitable paraphrases.