Halo: Reach

This is done on "Long Night of Solace". At the start, you will be protecting the ship from the enemies that are attacking it. After this, you will see the long purple Covenant Ship that you have to attack. Immediately go behind it and start shooting rockets at it's engines. Slow down by holding down on the Left Analog Stick to not approach the ship so quickly. After this is done, start taking out the enemies that they send out to attack you. Banshees can easily be taken out with the cannon, but the Seraphs are a different story. To easily take out Seraphs, use the cannon first to take out their shields, then hit them with one attack of the missiles. This will make them much easier and faster to deal with. Once there are only 5 enemy ships left, they will show up on your screen with red arrows pointing where they are. Take out the remaining ships to complete this.

Thanks to Sidedish120 over at x360a for the description.

I got this achievement playing co-op on heroic. If one person goes for the engines and the other works on the enemy ships, then when the engines are dead, there should be only a few enemy ships left. Simply help your partner dispatch the remaining enemies and you should have beaten the 3 minute time limit!
EDIT: If you are going to negative vote please tell me why so that I can provide a better solution. Thanks.

The mission is Long Night of Solace, on Rally Point Alpha.
After defending Anchor 9, you will get a cutscene and you will end up near the Corvette. Go far out and turn back so you have enough space to take out the 4 engines. After that, take out the Seraphs and the Banshees. The Banshees are easy to take out, as the rockets will instantly take them out, but the Seraphs are harder. You have to first take down the shield with the machine gun, then kill them with the rockets. Once you down to about 4 enemies, red arrows will point to the remaining ships. Once you are done, BLEEP BLOOP.

Video courtesy of RoosterTeeth

Mission 6 – Long Night of Solace

Mission starts at 0:49:32 in the walkthrough video below.

This mission is lengthy, even ‘speedrunning it’, and there just isn’t any way to avoid it really. You’ll start off making a D-day beach landing. If you follow along the video, you’ll be running past the bulk of this fight and just polishing off an Elite and a few Jackals at the end of the beach by the building. Once you enter the space fight, it’s semi-scripted, with each section requiring killing a certain number of enemies to progress.

You’ll eventually dock with the orbital defense station, then be sent back out to deal with an incoming Corvette (Covenant cruiser-class starship). This is when the timer for "Wake Up, Buttercup" starts; requiring you to take out the Corvette’s four engines, as well as its support craft within three minutes. I started this section with 15:51 on the clock and unlocked the achievement at 18:55. So either I just barely made the 3-minute cutoff and there were a few seconds’ lag time between when I thought it truly started/ended, or when you ‘restart checkpoint’, it resets the timer back to that checkpoint’s timer count. I honestly don’t know. If you’re struggling to get this achievement, I would suggest doing it on Heroic rather than Legendary, as the engines are easy to destroy, but the support craft can be more problematic on Legendary. Once the last support craft is destroyed (you’ll have waypoint markers on them when only a few are left), the achievement should unlock. If it does not, you’ll need to start the whole mission over to try again.