All mythic cards have upgradeable abilities; some of the earlier sets also have an effect that can linger for 3 turns. These haven't been implimented since the 7th set for each colour and are unlikely to comeback as it's now set 17-ish that is being released.
To upgrade a mythic card's skill you need 2 things. The first is to level up the Mythic card to level 5/10/15/20/25. The second thing you will need are libido gems; the amount depends on whether you're trying to reach level 2/3/4/5/6. Each tier costs 5 more than the last, as tier 2 costs 5 gems and tier 6 costs 25 gems. Usually the colour of the card matches the colour of the libido gem required; there are at least 2 exceptions (Sumi - Nuns; Dieter - Necromancers) where the wrong colour is needed.
To acquire these gems you're going to have to do one of three things:
1) beat a world boss stage that is a multiple of 5 to get that many gems of the colour they correspond to.
2) reach the end of the colosseum - defeat all 12 mandatory stages and go for the hardest optional stage: 45,000 pts. You can ignore the five optional stages that grant more cards.
3) get a top 2 finish in the daily rankings of an event.
numbers 2 & 3 see you recieve a special chest that grants 5 gems of the colour of your choice.
Don't assume that all mythics are created as equals. Some abilities are rubbish for quite a while, others are great from the start. See what damage they do with your hand before commiting.