In general this seems like a very good idea. I do have a few suggestions to get it working. The first one is a point that has already been addressed, but I would like to point it out clearly.
* Make your hated card alterable at will.
Now the argument here is that this will make your trial have very limited replay value, and my other suggestions primarily aim to fix this while still letting the hated card be changed so as to facilitate specialized tournament events.
* Make it so that you have to do the trial separately for each element.
This both prevents people from choosing the optimal element to breeze through it, and guarantees that a massive amount of play-content is added, as to 'complete' the trials you have to be a master of all twelve elements. However I have one more suggestion on top of this to
* Add a secondary bonus for defeating an element that you have already defeated.
And more than just coins since I imagine those will be gained through the trials anyway. My idea was something along the lines of a graphically altered version of a card. This way players who like specific cards can get their favorite cards selected to look unique. And considering you could get 6 unupgraded and 6 upgraded for a complete set, it guarantees that there is no 'end of content' anywhere in sight. No actual mechanics change with this would be implemented, it would just be a flavorful flair.
Of course, this might be a bit tricky and time consuming to even put a small sparkle into the pictures of all the elements cards unupgraded and upgraded. Other suggestions are welcome, but there should be at least 'some' key secondary stackable bonus to encourage continued trial use.
tl;dr: Read the Bolded things, these sum up the point and are the main purpose of the post.
I love this idea. Really really really love it.
I imagine the implementation as follows:
You can take a Trial for each element. Each tests your ability against that element through various challenges. Easy mode with Hard mode available after you beat it once in easy mode.
When you complete the trial, you can select a reward from a list. Mark modification allows you to have a mark of the element of the trial tuned to a certain card. You can change the card at-will. Each mark modification grants you a certain benefit, and all mark modifications can be turned on and off at will. Other rewards are available and more can be added in the future. However, most are "unlocked" once and that's it. However, there are two more options that are useful multiple times: an upgraded card of your choice (not broken: farming gods with Liquid Antimatter is going to be faster, and Arena grants thousands of electrum if you have a decent farmer; however, it is good for newcomers who play on easy mode and want to get their hands on a RoL Hope deck), or a card with altered graphic effects. These graphic effects are not necessarily new art (that's hard to come by), but rather manifest when you play the card. A flash of light, a noise, something minor that is there just for collectors' sake.
Alternatively, you can grant a score boost. Something like +1000 score on easy mode and +20'000 score on hard mode? But I'd like the graphic effect better, it's cool and gives a purpose for farming trials.