Well Revenge wouldn't count since you can't use it in the first game. But I don't see why Specialized isn't counted towards the total since they very likely will use those cards upgraded seeing that they bothered to spend a Strength to get that ability.
If we don't count the alchemy and nymph cards from the elements in an arena for a person with the Alchemist Strength, it would seem to make sense that we should at least count the cards that they have access to (Style cards and cards from Strengths/Weaknesses) that are alchemy cards. Again, if they bothered to choose a Strength/Weakness to upgrade and access Alchemy cards, it would make sense that they will probably use those cards upgraded in their decks which means they should count towards the Coward/Brave totals.
At least, that seems most logical to me according to the wording of Coward.