Alert 'new high score' on first attempt at level?

I currently alert the user of a “new high score” if achieved on a level.:2c:

I chose to have the first attempt at a level never alert the user of a new high score achievement because as you play through the levels (as a new user) you would constantly would get ‘new high score’ anytime you beat a level…not sure what is best here.

What do you think? I suppose this really depends on situation…which i didn’t really describe