Ladders/vines/etc. do not work for me. I've tried changing the key to climb them, but he just stands at the bottom, or whizzes right by them, and will never latch on.
To get the There Can Only Be One Badge easily, conquer the world til you find a "very rare and powerful" Occult Rune, which looks sort of like the atom symbol with a throwing star inside, which causes damage based on the opponent's defense, and hold on to it til you can use it on the best weapon available to you.
Then, once it's on the weapon, you can kill all of the leaders with two hits or so, as you'll do around 1500 damage a hit with special powers. It also turns you into a one man wrecking crew if you have area effect powers like Edgar's Smashing Jump, usually instantly killing anything around you.
The four other bases are practically worthless since you can only use them when they are at full shields, and using them takes them down to nothing. Also, the missles that suddenly redirect towards buildings when they're like 5 feet off the ground are impossible to stop, the guidance system should stop at a certain height.