For this achievement you need to
complete Chapter 7-2, which is only available after playing through the rest of the game to get to this point. There are 3 sections to beating him.
First Section - You need to dodge his ground pounds and raise platforms of Earth on either side. You can uncover them with Mustacho pounding or hitting them with a fireball. You must then make a water column to raise you to a ladder so you can reach the spot to make the lightning rod.
Second Section - Provide power to both columns. Dodge ground pounds again and get to the upper section again. Just hit Mustacho with a fireball to stun him, giving you time to connect the power with vines. You need to do this on both sides.
Third Section - Dodge Mustacho ground pounds again. After the third one, he will place an open palm at one side of the stage. Hit his hand with a fireball to stop his sweep. Then move away from his head area as he spews deadly breath down and moves from one side to the other. As he is spewing, hit him with a fireball in the head. Repeat this 2-3 more times and Mustacho will fall on the ground. This is your chance to attach the two side platform power supplies with vines to Mustacho's headpiece.
This ends the game as you have just saved your brother. The achievement will pop as the cutscene plays out before 7-3 Epilogue loads.
Try to do this without ding for another achievement. See Spilner's Guide for tips: