Very nice. At time of writing, I am in second place (I could have gotten first, but I was getting tired at this point). I kid you not, dying is the hardest part of this.
Here's my strategy (credit to Brushinobi for the idea):
Phase 1: Click in the center as fast as possible, taking care to not die. You want to level up as fast as possible, and you gain experience with airtime. You also want to keep the Wave bar as low as possible, which gains when you are touching the ground. Whenever you get a level upgrade, choose Azii, until it reaches 99%, then move onto Phase 2.
Phase 2: Now level up to Ignu level 3 by killing enemies normally (With Wave 3, you only need Ignu 3 to kill all of the enemies on the board). Then move onto Phase 3.
Phase 3: Here's where you'll stay the longest to rack up points. Click under the character's feet as fast as possible without double-clicking (double-clicking causes the character to try and get the closest sandwich). Whenever you get a level upgrade, choose Ignu, even though it's unnecessary at this point (you'll see why later). Do not level up anything else except Ignu, and be especially careful when you're just clicking super fast, not to accidentally level up something else. Continue doing this until you are satisfied with your points (or are about 75% the way to your desired point count), then move onto Phase 4.
Phase 4: Now here's the hardest part and the part that requires the most human control. Wait until at least Wave 4 so that the eyepatch sandwiches spawn. Now, attack the eyepatch sandwiches as fast as you can, being careful not to heal if at all possible. You will level up during this (which is annoying). Try to do it as fast as possible and choose Ignu only. If you choose anything else, especially Alchemy, Guen, or Urden you may make it hard or even impossible to die (yes, that's the goal!). If you want to, you can also wait for the Wave to get higher, but you might be there a while. Continue attacking eyepatches until you die.
Congrats! If you followed these steps, you have lots of points, and are probably higher on the leaderboard than I am. :-)