This is gained when boarding ships that you have damaged down to their last health bar (but not destroyed) using your Jackdaw. Once your men start cheering and you see the ship is on fire move up next to the ship on either side and you will be prompted to hold B to board. You need to be patient and wait for your ship to move right alongside who you are boarding or when you swing out you won't reach and will either end up in the sea or just on the rail. There is a rope at the far left and right of the jackdaw (when it is lined up sideways) you may have already used it when stopping at random islands to go grab treasure etc. As prompted hold RT and forward to swing on the rope then towards the apex press X (I still hold RT not sure if necessary) and aim towards one of the enemies. If you do it from a sufficient height they cannot defend it-so it's probably easier against the smaller gunboats/brigs etc as the larger ships have high rails.
*edit for those struggling you can also use the lift -head from the steering wheel down along the jackdaw, once up higher on the side you came from there is a rope hanging down from your platform you can use. I quite often using this one miss the boat entirely and land in the water on the other side hehe.
vI Demon Iv found that only ships with 10 crew or more seemed to count towards this achievement. If other people can confirm this that'd be great thanks. Also people don't always seem to be notified and sometimes only find achievements gained on manually checking under the achievement list.
Rez Ram states:
MAJOR TIP: Do NOT hold RT once you begin your swing. you need to hold it in order to grab on and go but I couldn't get the "ASSASSINATE" prompt when I realized I was still holding RT during my swing. It isn't neccissary and far easier to get the 5 kills if you release as soon as your swing begins.