"worthy of an encounter" vs "worthy of encounter"

This is an excerpt from my personal statement for law school. I assume that means creative and informal writing conventions apply. My question is whether the underlined sentence is acceptable in its current form. For some reason, I do not like the sound of "an encounter." Every source indicates my preference is grammatically incorrect. Given the informal context is this acceptable or not? And what is your personal opinion? Please indicate your credentials, if you don't mind.

t is my last chance because I do not desire to operate in the upper echelons of academia. I do not have the inspiring instruction I admire and seek in my instructors. I am a bulldog that belongs in the trenches. With a refined instinct, I seek those fights worthy of encounter. With a relentless disposition, the trenches are where I can obtain the justice I have been silently training for.