It's possible to get it working with HDT, see GitHub - borisbabic/hearthstone_hdt_linux: Contains instructions and code to get hearthstone with hdt running on linux. If you want to log into hsreplay you should have a working windows installation.
There is also GitHub - supertriodo/Arena-Tracker: Arena Tracker is a deck tracker that gives you a lot of extra info while playing Hearthstone. if HDT is an issue.
Source : [solved] Hearthstone with Deck Tracker / Multimedia and Games / Arch Linux Forums
Arena Tracker is also available in AUR
https://aur.archlinux.org/packages/arenatracker/