Hi, I've killed a few drakes with this strategy now, me and Duke Nukem came up with this strategy since we couldn't find any good guides online for killing the Drake fast.
How to Kill The Drake
You will need climbing picks, gliders and a weapon of your choice with tons of ammo (I prefer the bow because you can repair it with resources from your inventory whilst fighting).
Using your climbing picks and gliders (try to climb mountains and glide to the nearest Golden Age City/Building, bosses are usually there) find the boss and try to lure it towards random buildings until it gets stuck on 1 of the walls/buildings. Then you just get on a platform above it or in front of it and start shooting it to death :P If it gets unstuck then just repeat the strategy (usually doesn't get unstuck unless you move too far to the side or behind the Drake).
Oh it is also worth noting that the Drake only breathes fire downwards at a 45 degree angle, which is why it's attacks don't hit me in the video.
Also we have only done this a few times so far (worked very easily and fast though), so it might not work on every island, but i believe it does due to how easily we have gotten it stuck so far.
Here's some evidence of what it looks like whilst stuck: