Cards with the rarity 'Determination', reserved for characters strongly linked with Determination. These are the hardest cards to get in Normal packs, but are obtainable by expert players who reach Diamond+ in Ranked, as those ranks award the player with "DT Fragments". These fragments need to be used to craft DT cards instead of Dust. (You also receive Frags by selling DT's.) You need 4 Fragments to craft one. However, you can't choose the DT you want. When crafting a DT, you instead get a random DT monster you don't own yet. Once you have one of each, crafting another DT will give you a shiny version instead. These will also be given randomly and check if you already have a shiny version of it.
Final Packs are also another way to obtain DT cards, but the only way to get one (as of Beta 10.3) is by reaching level 200. However, they can also be given out during events. Final Packs, like Super Packs, give one of every rarity. But instead of a Common, a Final Pack gives a DT instead. (So it gives a Rare, Epic, Legendary and DT.)
A third way to obtain DTs is with the Daily Login Reward system, where logging in 28 days in a month will reward you with 1 DT Fragment. As such, if you just use this method and done right, you can craft a DT every 4 months, 3 DTs each year.
DT cards are represented by the red colour heart on the bottom centre of a card. They are limited to 1 of each per deck just like Legendary cards are. However, in Ranked specifically, you can only use 1 actual DT card at the most, not just 1 of a DT monster.
A special ability of DT monsters (which is shown with the DT icon in-game) is that they are immune to Silence. This ability is actually in the coding of the card itself and not an actual ability. As such, any new DT monster will also be immune to Silence, while all other rarity monsters can never have it.