I am not sure if しつこい would be appropriate in this context.
So here's the Urban Dictionary's definition:
A person who puts a large amount of effort into achieving a certain image, or counter-image, to the point where it is obviously contrived. Rather than achieving an image through genuine personality, the try-hard consciously attempts to fit a certain style through deliberate imitation, forced style, or scripted behavior. That is to say, he/she is trying hard to create an image.
Examples: An affluent, suburban dweller who makes great efforts to cover himself in tattoos and piercings; try-hard.
A person who wears certain items of clothing for the express intention of appearing "non-conformist", and flaunts it; try-hard.
Someone who purchases a motorcycle only to appear as a "bad-boy"; try-hard.
A person who shuns certain genres or styles of music or art simply because it does not fit his self-image, or the image he wants to portray; try-hard.
And ALC says:
A person usually of little talent who tries hard, especially through imitation, to succeed, usually to gain fame or popularity.
I have no idea how widely the term is accepted, but after reading them, I'm under the impression that a tryhard is not really a genuine hard worker (=努力家), but someone who puts effort in an easy and foolish way.
Some words and phrases have come up to my mind. All of the followings are nouns or noun phrases unless otherwise specified, and are more or less derogatory.
- にわか: Literally means "suddenness". As a slang term, it often refers to a certain unrespectable type of newbies who don't truly understand the subject they like, and act differently from other genuine fans. A にわか野球ファン may like to visit a stadium and shout wearing a baseball uniform, even not knowing the rule of baseball. A にわかロッカー may buy an electronic guitar but never practice it.
- 勘違い, 勘違い人間: As a slangy noun, it refers to a person who understands something terribly wrongly. Someone who firmly believes in something which is obviously incorrect to the others.
- 目立ちたがり屋: An attention seeker. A poser.
- まねっこ: A mimicker. A wannabe.
- 形だけ(を)まねる: (verb) To try to imitate only its appearance.
- 形から入る: (verb) To start with the appearance/superficial.
- 後追い: Literally "follower". Someone who tries to succeed by imitating others. For example, an unsuccessful "YouTuber" who tries to make a living by posting cheesy videos is a typical 後追い.
- 二番煎じ: Literally "second brew (of tea)". A recycled idea. ≒後追い.
- 才能のない努力だけの人, 努力しかできない人: A rather literal translation of "someone of little talent who can just try hard".
The four examples given in Urban Dictionary seem to be typically にわか and 勘違い to me, but perhaps you would have to combine more than one above to convey the nuance. For example: 「目立ちたがり屋のにわかファン」「後追いの勘違いユーチューバ－」「才能のない、誰かの形をまねただけの歌手」
One option would be 必死すぎ or 必死な人, since 必死 already means that someone is desperate (in this context, for winning).
But since some might take 必死 as a compliment, this link suggests 必死すぎて痛い which conveys a negative image. It would roughly translate to "so desperate that it's cringeworthy" (I guess that's what 痛い would mean in this case?)