It is legal. Attack You're using may get additional traits such as Doublestrike between steps and You will get to use this trait if it's present during additional strikes step..
The issue is when is the attack considered not made yet.
In Rules Supplement it's written:
Note: If a melee attack is canceled after the Declare Attack Step, the defending creature still loses its Guard
marker, if any. Once the Declare Attack Step is completed, the melee attack is in progress, and the mere attempt
to make the attack (approaching and engaging the enemy) will distract the defender sufficiently to remove the
guard marker. If the attack is canceled before the completion of the Declare Attack Step, then no “commitment”
was made, and no guard marker is removed.
This means that once the attack gets past Declare attack step it's considered to be made and it won't benefit from Badger Frenzy if the enchantment is revealed after that step.