You will be given a piece of Treasure Art every time you complete one of the 50 optional side quests. You can also unlock one for beating the game with each the six character classes, as well as one for beating the game on Infernal—the hardest difficulty. This amounts to a total of 57 pieces of Treasure Art.
It is very important that you unlock all 57 on a single save file. If you beat the game with several characters on a different save file, than you did with the others, you will need to clear them yet again on your main save.
Lastly, you do not need to complete all 50 quests on a single character to have them count towards this trophy; just on the same save. It's possible to do 30 on one character and the final 20 (different quests) on another, for a total of 50. However I strongly suggest doing all 50 on your main Infernal character because you will need all of the skill points you can get. Especially since experience plays no factor in beating the game with other characters.
If you are unsure which quests you've completed across all of your characters, you should refer to the Gallery in game as well as the Quest list. The gallery will tell you what quest you need to perform to unlock a specific piece of art, while the quest list shows whether or not it's available yet.
To see a list of all of the side quests and how to complete them, please visit this link.