The Highscore category is extremely straightforward; end the game with as many coins as you possibly can.
This category relies quite heavily on luck, and is not focused on speed whatsoever. The best way to increase the odds of you having the most amount of coins by the end of a run is by understanding where exactly you can get coins from. The best source of coins are, as expected, the beanstalk worlds. In theory the best strategy is to just get lucky, but the most realistic strategy is to reset runs until you can leave the first beanstalk world with a very high above-average amount of coins. The average amount of coins is 626, and the maximum amount of coins is (virtually impossible odds) 2,126. Leaving with over 1k coins is definitely lucky, and leaving with over 1.5k coins is incredibly lucky.