King's Bounty: Armored Princess

Moreover, if I can't defeat the easy boss, I won't be able to defeat the strong ones!

Well, I wouldn't say that the Driller is the easiest. The Spider and especially the Toad are much easier, in my opinion.
I played on Hard, and after several attempts to defeat the Driller (as a Mage) before swimming to Umkas and Elon, I gave up on this hopeless endeavor. I killed him near the end of the game, when he went down without any losses. Moreover, I was playing more for fun than to finish it quickly, so I didn't bother with extra trips back and forth. But the last three bosses are really much harder...

Is it really possible to beat the highest score in the leaderboard on Easy difficulty?

I don't think it's possible on Easy, you have to try hard on Normal, and on Hard and Impossible, it's hard not to beat it :)