Story related, cannot be missed
Chairman Drek is the final boss in the game, you fight him on the last level on Planet Veldin. Boss fight Walkthrough below:
First Form - Drek uses several different attacks; he will shoot out missiles, which can be easily avoided, and fire exploding flame bombs, which again can easily be avoided.
First up, swing to the platform Drek is on using your Swingshot. Use the R.Y.N.O here to finish this form of Drek in just a couple of shots.
Second Form - Drek's second form is a lot like his first, except Drek will have a new attack: he will throw mines. The mines will chase you if you get close to them, but you can attack them with your wrench without taking damage, but be careful because he will still be attacking you with his original two attacks as well. Take out the R.Y.N.O and after a few shots he will retreat to the third and final platform. Go from piece to piece again and get out your Swingshot. Be aware that the last platform will break away without you even touching it.
Final Form - Drek has another new attack, in which he sends out Drones to attack you. He will also commence a countdown at intervals during this fight. When this happens you will have to jump and slam down on the lock in the middle of the platform; this will stop the countdown. Immediately shoot Drek with the R.Y.N.O. When the counter gets down to about ten seconds, slam the lock down and Drek will chase you with a heat ray. Just continue blasting him with the R.Y.N.O and he will flee after a few shots. Keep attacking him until he does the countdown again. Slam it down and keep at him with the R.Y.N.O and he will set the timer yet again. Hit the timer and finish him off with a few more shots.
First Form - Use the Blaster first up and hit him as many times as you can. He will begin his volley of attacks, and once he is done get up close and hit him with a Visibomb. He will break the platform you are on and will eventually go to the next. Chase him by jumping from piece to piece of the platform until you need to use your Swingshot again.
Second Form - I suggest using the Devestator and Blaster on this form of Drek. Watch out for his mines and missiles combo, as you will have to dodge all of those mines as well as the missiles. If he uses a flame bomb when there are mines on the ground, the mines will be destroyed which only helps you. Keep at him and dodge his attacks while focusing on him. If you get low on ammo, purchase more through the Gadgetron PDA. Eventually he will retreat to the third and final platform. Go from piece to piece again and get out your Swingshot. Be aware that the last platform will break away without you even touching it.
Final Form - You will need as much health here as possible, preferable 8 health circles. Immediately start shooting Drek with the Devestator/Blaster. When he is throwing bombs get close to him and use the Tesla Claw, it will be your best friend in this final stage. Stick close to Drek, jumping over shockwaves and using your thrustpad to avoid the missiles. All the while keep at him with the Tesla Claw. You will need the Gadgetron PDA here. When Drek sends out the drones, switch back the Devestator. There are grind rails around this platform so feel free to use them to avoid a few of his attacks, while firing the Devestator at him. Repeat this process, while slamming down on the countdown button, and Drek will eventually go down.
Trophy will unlock shortly afterwards, you now want to accept challenge mode.
Member lukey52 has provided this tip for defeating Drek:
For what it's worth, when I get to Drek I had 1 bolt so couldn't buy stuff had to make do with what was dropped.
I found the Pyrociter to be a total beast. Simply wait for him to fire out the 4 explosives and after jumping each wave unload into him. The first 2 sections take literally 1 minute and save all your ammo for later.
Even in the final area it's still possible to do the same thing. I only needed to use the Devastator once he was only ever keeping distance from me. The entire fight lasts a few minutes at most.