fairy fire decks are reliable method for scaling damage. The defender of the cosmos pack happens to to have a couple cards that not only increase their damage but also keep their damage increase between matches so if you can make a good deck from that pack early you can keep up your match winning speed without things slowing to a total crawl.
While cards that permanently grow your max hp exist the the booster is locked behind an absolutely diabolical side boss that'll make the current you just outright despair. There's a couple more resources for increasing hp though. There's a black market vendor at night time arena inside with 3 extremely useful items. Also win some gambling matches at the casino in order to access the VIP lounge which has a means of quickly increasing max hp if you're willing to sacrifice height.