Run to the end of the first level as fast as possible.

When you reach the elevator, wait for the "next level" and other button to appear.

Click the "next level" button as fast as possible 23 times before you go to the second level. The two best ways to do this, are to either get some form of click counter that you reset before the run, or just learning what 23 clicks feels like.

When you get to the final level, kill all the guards and get up the stairs (you will probably bonk on the top two, haven't really found a faster way up), then attack Baron Battenberg. You can kill the guard at the top from the bottom by bouncing your shot off the top, which saves no time, but feels cool.

You obviously want to go for the blue nodes on his "Steam-powered Batter-Berger", which will lower his health one point at a time, which you will need to do 10 times.

You can probably manage to get two shots off before he gets around the right side of the arena, then back up and shoot up and to the right and hit him before he gasses you from above. Then its a matter of spamming and damage boosting till he dies. The best time to get shots off is when he's leaving the left quadrant and lowering himself to the middle. While you will have to avoid wasting your shots on guards and missiles, his pod his moving very slow there, and to beat the current record you'll have to get him before he starts moving away from the middle.