That is not a sentence because it has no subject-verb combination. It might be a subordinate phrase, but it is hard to tell if it can be even that because "reach" looks like a verb without no subject. "In the hope(s)" is an adverbial phrase that wants to have a verb to modify. I'll use "play" since you seem to be speaking about an athlete. "He played in the hope he might be a champion and place first." Modal verbs like "might" are excellent for expressing wishes and possibilities.

Hi Robson, me again! haha The phrase is close, but it could be clearer. "In hopes of becoming the champion and reaching first place." That way, it’s a bit more straightforward. all the best,