Did Kirito lie about being the *best* beta tester?
You can think that's a lie, but not totally.


  I made it higher than anyone else during the beta test. The reason I knew the bosses skills is because I fought monsters with katana skills on floors far above us.


There are two possible interpretations of his claim:


Kirito made it to higher floors than anyone else.

This is incorrect, because you cannot go to higher floor without defeating the boss first. And, after you defeat it, everyone else can go to the next floor through the teleport door.
Kirito have more experience than others.

This is probably correct, because from Light Novel Volume 1 - Chapter 2:


   The two months of beta testing were like a dream. At school I thought endlessly of my skill set, equipment, and items. I ran all the way home as soon as school ended and dived till dawn. The beta test ended in the blink of an eye. On the day my character was reset, I felt a sense of loss as if half of my actual self had been cut away.


Because of this, you can assume that Kirito had spent a lot of time on the game,  maybe more than others. Maybe he compiled more floor map information than other players... maybe, he knew more mobs, but he couldn't know mobs or bosses from upper floors. All information which Kirito knew was also available for other beta players if they tried to view it (maybe, but unique quests were unlikely to be made public).

There's no info about boss defeat in beta, but there probably wasn't any boss defeated by Kirito only (but that's my opinion).