『 "The Hare and the Tortoise』"

The race got startedbegan.

"Started" is fine, too, but you don't need to use "got."

Peter pretended to befall asleep on the way to the goalfinish line and lost iton purposely.

"Fall asleep" sounds best to me. Also, for races, we say "finish line." Goal is used for other sports, such as soccer and basket ball.

Tortoise won for the first time.

We will continue to compete and Tortoise will aim at afor consecutive winner.s,” Kevin said so and left Peter.

"Wins" should be plural.

TheyYou're all ridiculous!” Peter spat out and quickly left there for a new land.

If Peter is saying this to the hares, "you're" is best.

"Left there" sounds a little awkward to me.

Hare country and Tortoise country hold a marathon race every year to compete which one runs faster.

I might say "to see which animal runs faster." The "one" here sounds like it's talking about the countries, but countries cannot run.

Peter, the representative runner of Hare, said to Kevin, the representative runner of Tortoise, “No matter how many times we compete, Hare wouldill win for sure, s. So let's stop such a stupid race.” Kevin said back, “No way!¶
"No way," replied Kevin.

"Tortoise will win for sure.

If we lose, we will challenge you again until we will win!”

The race got started.

You can also simply say "the race started," but this is fine.

Peter pretended to be asleep on the way to the goal and lost iton purposely.

Let's stop our countries from holding meaningless races noany longer.” “Nope!

We will continue to compete and Tortoise will aim atfor a consecutive winner.,” Kevin said so and left Peter.

Peter was accused ofblamed for the losts by Hare citizens and expatriated from Hare (country).

If you want to use the word accuse, you would write the sentence like this:
"Peter was accused of losing the race on purpose..."

“I think the aimour goal is wrong.

I would say, "I think we are misguided."

It's not always nicebetter to run faster.

If you mean that running faster is mean, then the original sentence is OK.

Tortoise has its own qualities.

Or, "Tortoises have their own qualities." But I think "Tortoise" is the name of the land, so it's OK the way you wrote it.

Furthermore, if Hares wants to improve themselves, they should challengompete in other things like a contest of wits.

The word challenge needs to have an object. For example, "challenge you" or "challenge something." It isn't used by itself very often.

They're all ridiculous!” Peter spat out and quickly left there for a new land.

If he's talking to the Hares, he should say "You're all ridiculous!"

Hare country and Tortoise countryThe hares and the tortoises hold a marathon race every year to competsee which one runs faster.

"The hares" sounds more natural than "hare country." I would either write "to see which one runs faster" or "to compete" but not "to compete which one runs faster."

One year Peter, the representative runner of Hfrom the hares, saidys to Kevin, the representative runner of Ttortoise, “No matter how many times we compete, Hare wouldwe will win for sure, so let's stop such a stupid race.” Kevin said backreplies, “No way!

You could also put the whole story in the past tense:
One year Peter, the representative from the hares, said to Kevin, the representative tortoise, “No matter how many times we compete, we will win for sure, so let's stop such a stupid race.” Kevin replied, “No way!
I think present tense is more natural

The race got started.

Or
"The race starts" if you switch to present tense.

Peter pretended to be asleep on the way to the goal and lost iton purposely.

Or
Peter pretends to be asleep on the way and loses on purpose.

We will continue to compete, and Tortoise will aim atfor a consecutive winner.” Kevin said so and left Peter.

Peter was accused of the lost by Hare citizenthe other hares and expatriated from Hhare country.

Tortoises has itsve their own qualities.

Furthermore, if Hhare wants to improve themselves, they should challengompete in other things like a contest of wits.