Legendary-Free PvP Queue
The most obvious comparison for this game is to Pokemon. In Generation 4/5, online battling (much like Haypi) was introduced. As it turns out, there is a "tier" system that bans over-the-top legendaries to keep a safe, healthy metagame going (considered "Ubers" by the competitive community).
Right now, the state of Haypi PvP is essentially people with Mewtwo and Ho-Oh (customers who have hundreds of dollars to drop on the game) battling against people with Alakazam and Charizard (people who can't). Obviously, paying customers pay-to-win. This is obviously bad game design, but I'm not going to complain about it here.
What I am going to do is make a suggestion to remedy the problem: create a no-legendary (i.e. Epic and lower) dedicated PvP queue/an option to disable them, in addition to the already existing "anything goes" queue for people who care to play with their purchased monsters.
The biggest problem with this is, of course, that it will fragment that already slow PvP within servers. This is a problem for which many others have already suggested a remedy: combine servers or at least allow some form of cross-server PvP.
That said, I think I would enjoy this game much more knowing that my well-thought-out team of S Epics will not lose to some 12 year old kid who stole his parents credit card and has a bunch of Cerberus (Cerberi?)
It would be greatly appreciated if a developer commented on this, so as to show that they do, in fact, actually read these forums.