Perform 20 fear takedowns.

Use 100 Quick Gadgets while in free flow combat.

Take on the heavy artillery reinforcements.

Fight for your sanity.

Obtain a key by completing the sixth Riddler trial.

Obtain a key by completing the fourth Riddler trial.

Interrogate the Militia APC Driver.

Restore power to the bridges of Gotham City.

This is proof that you've collected all items, most of which is equipment. The core concept of equipment is the combination of stat boosts and embedded skills. Items you initially dismissed might in fact hold the key to defeating the most formidable foes.

This is proof that you've created an item of equipment with the same skill in all four slots. That's at least a Stack 4 bonus skill right there! You can do the Bonus Dance. We won't judge you.

You defeated some sort of people who came from some sort of place using some sort of means. This is some sort of proof of that. Sort of.

Either on (at least) your 3rd playthrough or in Hard (or greater) difficulty, win the final battle without retrying! If you can't feel alive without the icy glare of death at your back, we recommend you start the game in Hard right away! Playing in Hard or higher increases your likelihood of obtaining double-skill equipment!