Story related, cannot be missed. You fight the Sentinel after exiting the Project Wideawake facility (level 3). Tips on fighting the Sentinel: the Sentinel Mark is a tough guy to take down. He will pound on the ground with both his hands and feet, this will send shockwaves that will knock you off your feet. If you jump you can avoid these shockwaves. Lunge towards the Sentinels feet and slash away until they explode, then repeat this process with his hands. He will make a sweeping movement over the ground a few times, at these moments, let him pick you up and slash away with or . As soon as you have demolished the Sentinel's hands and feet it will take off, with you clinging onto him.
When the cutscene ends start the freefall towards the Sentinel. Make sure to steer clear of the large pieces of debris or fly through them by pressing . The very large pieces that come off the Sentinel cannot be destroyed and have to be evaded. You first have to destroy its two engines and then pop up a shield on its chest. Once you get to this section tap like crazy with , to knock the shield of the Sentinel. If you are not fast enough, it will blast you off and have to do it again. Once you knock of the shield a cutscene will start where Wolverine destroys the Sentinel.
Also see the description for "Threading the Needle" to get another achievement during this boss fight.