Highest level reached with levels won in a row. So basically, it’s the highest level category, but with no losses. You can check that by seeing if the level icon in the menu is gold or not.
I disapprove this proposed category.
The gold level icon is rewarded when you beat a level on your first try and only your try. So basically, you have only one shot at it if you don't want to go with the hassle deleting the game and re-downloading it just to try again (that's also why we authorize replay of levels on the boards). Furthermore, past World 1, passing levels on first try is more reliant on good luck and churning out cash than actual skills.
Also, I would ratter avoid to add another pure "Score Attack" with no speed component to the boards; I consider the Highest Level consider as grandfathered in that regard. It is mainly a leftover from the time where Dong left the moderation but before me and Oz really took over. We kept it in because it seemed to make the rest of the community happy.