One of the four Legendary ships in Assassin's Creed 4: Black Flag is El Impoluto (which is Spanish for "The Big Polluter"). This is a video of straight up naval battle - no exploits. The main trick to getting it done in 4 minutes is to go on the offensive. I didn't brace often and nearly ended up getting sunk because of it. A few notes:
0:18 - Use mortars when at a great distance.
0:28 - I intentionally let El Impoluto ram the back part of the Jackdaw. This spins the Jackdaw around so we have a clear shot at the stern of El Impoluto as it leaves.
0:50 - Hold to fire Swivel Guns at weak points when prompted. I had the HUD turned off for this video and missed some other opportunities to do this.
1:25 - Pull right alongside the Legendary ship to use your Heavy Shot. This is like Broadside Cannons except you don't aim, just fire.
2:00 - If it gets on your 6 o'clock, deploy Fire Barrels. You can aim them a little to the left or right as necessary.
3:25 - After getting rammed one more time, I finished off El Impoluto with a 1-2-3 combo of Heavy Shot, Swivel Guns, and Broadside Cannons to the stern. That'll teach 'em to quit polluting the Caribbean.