These Ruling(s) have not been confirmed as applicable to the TCG.[Notes 1]
You can activate the effect of Battlin' Boxer Sparrer during your Main Phase 2. The effect mentions that you cannot conduct a Battle Phase after you use the effect of Battlin' Boxer Sparrer. However, that doesn't prevent you from conducting your Battle Phase before using the effect. If you could not conduct a Battle Phase at all, text similar to "You cannot conduct your Battle Phase the turn you use this effect" would be used instead.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.