Inscryption

This is a fairly simple action, but takes a bit of setup to carry out.

When you first come up against The Angler for the second Boss Battle in Act I (See Grizzled Angler  for a full boss battle walkthrough), you will be introduced to his Fish Hook and the possibility of him stealing one of your cards. Once The Angler has been bested, your next run will start with your opponent giving you The Angler's Fish Hook. For every Act I run following this event, the Fish Hook will be available as a backpack item that may be given to you at random, Once you have it in your pack, consider keeping it for your next Angler encounter, because the Hook is only available once for each run and will not appear again for your backpack.

What you will need to do is allow The Angler to take one of your cards during the first round of the battle, and then follow it up by stealing the card back using the Hook. The trophy should be awarded to you right after you perform this action. 

I was successful in getting this trophy when fighting the final boss of Act I while he was disgused as The Angler after stealing one of my cards. You can see this work in the video below as well as a quick guide to Squirrel Wrangler  and Gruesome Encore  (slight spoilers ahead):
 

This is also something you can save for Kaycee's Mod, as you will have at least 13 opportunities to fight The Angler in all of the time you need to spend completing runs of the Act I challenge mode, as well as the Final Boss of Act I as seen above. Just make sure you are not selecting "No Fish Hook" as one of your Challenge modifiers when you start a run and you should have access to the Fish Hook for The Angler Fight. Last small item to note is that the boss battles are randomized in Kaycee's Mod so you may fight The Angler first, second or third along your path.