A brief Hero Hunters Tier List with related information that can help shed some light on things. Heroes can have up to 10 stars which is an indicator for how strong they are. It looks like though you can only get a hero with a 7 star rating at the most. It looks like the developers have only made star ratings up to 7 so more content is probably on the way, though it has been some time now that the game has been released.
Once you have a certain character you will not be able to increase their star rating. The best thing that you can do to improve stats is get a better hero. Using chests in the shop which are purchased using gold can have a great selection when it come to getting heroes and you don’t have to collect all of their shards.
As far as a tier list is concerned you can view the stats of each hero in the selection screen even for the ones that you don’t have. All you have to do is select the hero you would like to look at and then you will be taken to a screen with more information.