I'm trying to make these very short and to the point, please don't feel as though I'm being overly critical. I know you said that it's not supposed to be like an English major wrote it, but you can always make it better, so while I won't try to be overly picky, I will say everything I think can make it better. Also, while I don't think it influenced my critique, I'll admit outfront that I am an unashamed atheist, but I understand that's not what this is about, so I'll try not to make any mention of it.
"The person who influences me the most, as well as my decisions, is a man most simply known as Jesus."
I would restructure this "The person who influences me and my decisions the most". The way you have it is unnecessarily wordy.
"Whether or not you believe he was perfect, you still have to admit that his life was a great one."
One really shouldn't use "you" in writing. I'd restructure this to the effect of, "While he may be a polarizing figure for some, he was undeniably a moral and spiritual leader in his time." This restructuring also helps avoid confusion over what I feel is an undefined definition of great.
"His teachings still influence millions of people today. He always showed love and compassion for every person he met. He always put God ahead of everything else, which is something I strive to do every day. He was also a very courageous man. He faced persecution and death, but still continued to do what was right. He was a great man, and his actions and teachings are what I try to emulate every day of my life."
Your sentence structure here is very repetitive. Try combining some of the sentences and using transition words between them: "Moreover, he was a very courageous man, facing persecution and death, yet still continuing to do what is right."
The transition to the second paragraph again is pretty brusque. Try some transition words. They're helpful. Paragraphs and sentences that don't flow well are really a pet peeve of mine. If you don't understand what I'm trying to say by this, please tell me and I'll try to elaborate.
"He showed love and compassion to the world, and some people showed it back, while others didn’t." I would move the while so that it reads "and while some people showed..." Doing that helps indicate the logical jump between his actions and other people's actions. Moreover, I'd add something along the lines of "Despite this, Jesus's love was universal". On it's own, the fact that other people were mean to Jesus doesn't really support why Jesus was a nice guy without it.
"I sincerely wish that the rest of the world would try to act like Jesus as well, because then I believe the world would be a truly better place." A few things: I would remove the word sincerely. It sounds a bit trite. Wish is OK, but if you could find another word, I would try to. I'd also try to offer support as to why you think the world would be a better place if everyone acted like Jesus. It doesn't have to be a paragraph, or really anything more than a clause, but I think it needs to be there. Lastly, while it can be acceptable in a personal essay like this, you really shouldn't use "I believe", "I think", or anything to that effect. As the author of the essay, it's assumed that what you're saying is what you believe. That being said, it's difficult to write an essay about a mentor, especially a spiritual one, without saying "I believe", so it's rather acceptable in this context. I wouldn't use it unless you absolutely had to though.
"That is something that I try to do" You've used this phrase a lot, I'd try to at least rephrase it, or remove it entirely and restructure this. Other than that, it's very difficult for me, as an athiest, to critique this section.
"Jesus exemplifies courage". Add transitions; "Lastly, Jesus exemplifies courage."
"I believe that he died for our sins, but whether on not you believe that, he did die for something, and it took a lot of courage for Jesus to willingly be killed, when he could have stopped teaching a quite a while earlier to avoid it." Ironically, while you broke two of the rules I previously mentioned ("I believe" and "you") I thought this was a great sentence. But it can be better! I would change it to "I believe that he died for our sins, but even if you don't, he did die for something. It took a lot of courage for Jesus to willingly be killed, when he could have easily and legally avoided the sentence. Jesus was willing to die for his beliefs, which is something that I tremendously admire. (Assuming you do, actually, admire that.)"
The last paragraph: Same comments I've had before. Combine sentences to vary sentence structure, avoid repeating yourself, try to avoid "I believe" "I wish" etc. if you can. But it was a pretty good conclusion, things I have already mentioned aside.