Earning this achievement is very simple.
There are two sections for this boss.
The first section has you taking on the boss from the top to the bottom. First, have the Majin stand there and get hit while you dash to the left side and hit away at the spider's legs. The spider will get annoyed by your assault and head to the center. While he is making his way to the middle, command the Majin to execute the wind ability and if done correctly, the cage should crash into the spider and he will plummet to the bottom. Jump to the bottom and immediately begin hitting him with your staff multiple times until he rises back on his feet. As he hits the air, make a beeline for the ladder that's behind you and climb them as fast as you can. By this point, the spider should be on the right side, so head over there and hit the spider's legs one more time. The spider will again get frustrated with you and makes his way to the middle again. Go ahead and command the Majin one more time to use the wind ability and knock him down with the cage. Follow him to the ground, then constantly hit him until the first weakpoint is finally killed.
A cutscene should ensue, with the Majin joining you after pushing the cage with his Wind ability and hopping onto it, making it crash and hit the spider.
Once that cut-scene ends, the second part of this boss fight begins. At first, I didn't get it and I died, but I smacked myself in the forehead after realizing how easy it would be after figuring it out. You need to hit any of the legs multiple times until the spider is close to losing his balance. You'll know when that happens when the Majin tells you that his wind ability should bring him to the ground. Go ahead and command the Majin to execute the wind ability and he should fall down. Then hold down the right trigger, point to the cage, and hit X to command the Majin to take that cage and smash it on the spider's head. Once that's done, he will rise back to his feet. This time around, the spider will unleash a jumping quake move that will hurt a lot, so you'll have to jump to avoid it when that happens. Repeat the same strategy, as in hitting his legs until he's losing balance, then bring him to the ground with the wind ability, then finally commanding the Majin to smash his head with the cage one more time. If done correctly, you should be able to finish him off for good, so when it comes on the screen, just hit B and he should be out of the picture for good!
Once the ensuing cutscene ends, the achievement should unlock right then and there. Have fun and good luck!