Rate the first sentence above you

Very poetic. Maybe not the first sentence in a poem, but maybe the second or the third part of the poem.
Makes you feel that the person it was written about was very lonely. 7/10.

"Are you kidding?" He said, looking utterly confused, while Peter was completely calm and simply said:
"Yes, I brought an elephant."

That's hilarious dialogue. Now I'm wondering what your story is about.
9/10
I'm not terribly attached to my sentence, and figure I can do something way more eye catching. Please help!
"He quietly walks up on stage, the guy that will be introducing the new president of America."

7/10 -- love the concept, but would love to get more about the character with mannerisms or something to give me a connection to him.

Jerica leaned over the castle wall, loosing an arrow directly into the face of the Nykerian soldier climbing up the ladder in front of her.

Solid 9/10. Excellent use of proper archery terms, Shady! It feels like a chase scene, which adds stakes. Overall, good job!
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Tonight, I was finally going to kill that guard.

8/10 -- @AlmostImmortal I like that it's short and sweet and immediately draws you into the character's goal and intention. Would be nice to have more of a sense of place, time.

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It was one of their good days, after the rain, when the jetty was covered in shining pools like mirrors and it felt like nothing could disturb them.

9/10. @Liminality Obviously some of this could be better explained if I had more context but I throughly enjoyed the description. I can feel some real power behind some of the words. I’m sure not sure at this point what’s so important about them.

Gutters filled with racing brown bullets of water, small puddles trundling into the ditches below. Ditches that soon flowed with streams of skipping raindrops that were captured by the rumbling old rivers that flooded roads and tipped over cars, cracking bridges as it tumbled downstream. Water roaring as it tumbled out the river’s bearded mouth. The ocean threw a tantrum of caterwauling streams of waves, beating its fits against the old black rocks.

5/10 @Moonglade honestly this seems like description dump, and makes it hard to read and digest properly. This is a paragraph more than one sentence and I think that adds the difficulty on absorbing what you're wanting to convey here. I do like your last line, though.

"The ocean threw a tantrum of caterwauling streams of waves, beating its fists against the old black rocks." <-- honestly, this is all you need to make an impact with your words. The rest of the paragraph is a bunch of flowery but hollow language.

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It took Railyn Yora a good two weeks to get up the courage to tell his dad that he applied to Lux Academy, and it took even longer to admit to him that he had gotten an acceptance letter to Lux Academy.

A few years late but I rate your first sentence a 7/10. I like it and I would continue reading but it is not the most exciting sentence written. Tho I do like it as I said.

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"There's a monster under my bed,'' those were the first words spoken to Esse that morning

7/10, depends on how it is expanded :p i think it's rather vague

Once, you watched a documentary about animals in the wild whose companions died so suddenly that the animal left behind was unable to leave the corpse, perhaps even unable to comprehend or process that the body leftover would never move again.