In 2013, Com2uS, the game’s developer, introduced the Heroic Animals. They’re the fifth and final animal needed to complete a regular (re: not event-specific) collection. Unfortunately, even after 4 years, only 14 out of the 60 collections waiting for a Heroic type can be completed.
For some reason, there are also these impossible achievements that no one can fulfill because the requisite fifth animal doesn’t exist:
Perhaps they’ll eventually be doable but it would be nice if they could remove these in the meantime. 😛
I believe Com2uS didn’t consider the bigger picture when they created the Heroic Animals since, unlike the typical ones that just roam around the map or fill speech balloons popping up above their heads with inane statements, they possess skills that can usually help gameplay aspects such as allowing animals to instantly level up or increasing the chances of successfully obtaining a higher tier animal through breeding.
Inserting a bit of a tangent here: There’s one oddity among the Heroic types. The Heroic Bearded Pig, also known as The Crazy Doctor, can actually harm crop efficiency by tacking on a negative percentage value to crops causing the player to lose out on profit and experience. Thankfully, its skill effect can be cancelled before any damage can be done. However, this would mean that the player wasted Hearts on the Heroic Bearded Pig for nothing. 😐
It could be my luck but I do end up with the negative result more often than the positive one. 
Unless you have Hearts to spare, I advise against gambling on this nutty pig.
Here’s an image of it, by the way. 😀
Anyway, new Heroic Animals used to come out on a consistent basis, but it’s not surprising that this stopped a few years ago. After all, it takes time to think up useful abilities that will keep the game in balance. Still, this lull feels rather lengthy. I’ll give them the benefit of the doubt since they did eventually come up with third dog for the Dog collection years after the first and second ones. (It’ll probably take another couple of years before the Talking Dog shows up. :P)
In the interim, Com2uS has opted to keep churning out new limited time and event-based collections with increasingly insidious money-making ways.
koukoupuffs 