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; however there are at least 2 exceptions where the wrong colour is needed (Sumi (B) - Nuns (R); Dieter (R) - Necromancers (P) ) .
To acquire these gems you're going to have to do one of four things:
1) beat a world boss stage that is a multiple of 5 to get that many gems of the colour they correspond to . e.g. stage 5 = 5 gems.
2) reach the end of the colosseum - defeat all 12 mandatory stages and go for the hardest optional stage: 45,000 pts (green banner). You can ignore the five optional stages (red banner) that grant more cards. You'll need a high tower rank and large deck to even consider this.
3) get a top 2 finish in the daily rankings of an event - Usually 32,000 points as a minimum for 2nd.
4) pay $50 for the upgraded buttpass during an event and reach step 8.
Note: #4 only worth considering if you can reach at least step 16 of 17; then you can also collect 5 card pulls - 1 of each rarity of the same element as the current event. e.g. Light themed event = light only selection. The card pulls will give you 8-10 options irrespective of the rank.
numbers 2 - 4 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.