This is just a random attempt. Please inform me of any mistakes I have made.

"Dum la tago, mi estas junviro ordinara. Tamen, dum la nokto nigra, mi iĝas la Vespertviro. En vestoj grisaj kaj sen flugiloj, mi batalas.

Mi kontrauxbatalas krimulojn bone, kaj mi timigas ilin kial diego kiu reĝas homojn.
Batalante, mi venkas je ĉi tio ludo."

I'm trying to say:
"During the day, I am an ordinary young man. However, during the black night, I become the Batman. In grey clothing and without wings, I fight.

I fight well against criminals, and I make them afraid like a great god who rules over humans.

Fighting, I triumph in this game."

Also, did I use "kial" correctly? I wonder if the way it is written describes the criminals rather than my actions towards them.

Again, thank you for any help.

I'm not going to post a corrected version but here are some hints and ideas to help you correct things yourself.

- I am not sure if it's only for effect that you did it this way, but though Esperanto has flexible word order, normally adjectives come before nouns (unless you're trying to make a special emphasis).

- junviro is a little strange. Most people would just say "juna viro". But the more common word for a young man is actually "junulo" (a youth). Depends on how much you want to emphasize the youth or the manhood, that's your call. Junviro is perfectly understandable and grammatical, just not a common choice.

- grey is "griza" with a z.

- kial means "why" or "for what reason". You need a different word for that (hint: you were close).

- rule is "regi"; regxi is to be a king

- the word "tio" can't describe a noun. If you're going to use "that" all alone, then "tio" is ok (example: "I hear that!" ), but if you are going to say "that [noun]", it has to be "tiu" ("I hear that noise!" )

erinja:
- I am not sure if it's only for effect that you did it this way, but though Esperanto has flexible word order, normally adjectives come before nouns (unless you're trying to make a special emphasis).

Perhaps Hound_of_God has taken a course or two of Spanish? I initially found it strange to not change up the word order because Esperanto reminded me so much of Spanish.

It's common and it's not necessarily based only on Spanish. When I used to tutor, I noticed that certain students had obviously studied German because they kept putting the verb at the end of a sentence! I think sometimes you study one foreign language and you think right, Esperanto is probably more like (that other language) than English, so I'll do this like (that other language). It's hard to make yourself think that in many respects Esperanto may work more like English than like the other foreign language that you've studied!