Hi, Newton! I enjoyed reading your experience with the claw machine! ^^ I wish I could be as lucky as you are when it comes to that. ^^ Here are my corrections. You could also apply these corrections next time. Good luck! :)

Yesterday, I did claw machine game.

>> Yesterday, I played the claw machine game.

I had only 2000 won.

>> correct! ^^

So, I had to do very carefully.

>> So, I had to play carefully.

The doll was under another doll.

>> This is correct. You can also say "The doll was under the other dolls", since the claw machine is full of dolls. ^^

I can get two dolls.
>> I could get two dolls at the same time.

(You are talking about the possibility of getting two dolls in one strike. Like the saying, "hitting two birds with one stone" ^^)

It was poketmon, named "Pokemon kkobugi".

>> It was pokemon kkobugi.

(You can also use the English term for that. " It was Squirtle.")

I did hard but it was failed.
>> I tried my best but I failed.

I was so angry, so I came to home and take money 4000 won.

>> I felt upset, so I went back home and took 4000 won.

But I failed.

>> correct!

So I wait and wait and my parents came.

>> I waited patiently for my parents to come home.

 
So, we went together.
>> And we went there together.

And we got 2 dolls.
>> correct!

Yehey!!!.

>>correct!

I felt fantastic, and I put on the doll in bag ring.

>> I felt fantastic and hung the doll on my bag.

I want to get another pokemon "Pyri".

>> I want to get pokemon Pyri next time.