1. Wonder Girls are doing their best to be a world star.

2. Wonder Girls are doing her best to be a world star.
3. Wonder Girls are doing the best to be a world star.
[Which one is grammatical?]

Wonder Girls was a girl group composed of five girls.

I assume Wonder Girls are more than one girl.

The correct statement would be:

Wonder Girls are doing their best to be world stars.

Or --

The Wonder Girls group is doing its best to be a world star.

Have you ever wonder why when addressing Nigeria,they make use of "her"...its mostly like a word that best defines reproduction as a group....i think #2 is grammatically correct

Out of the three sentences provided, the first sentence is the grammatically correct one:

1. Wonder Girls are doing their best to be a world star.

In this sentence, "their" is used as a possessive pronoun to indicate that the Wonder Girls, as a group, are collectively doing their best to become a world star.

The second sentence is incorrect:

2. Wonder Girls are doing her best to be a world star.

Here, "her" is used as a singular pronoun, but "Wonder Girls" is a plural noun. The pronoun should agree with the noun in number, so it should be "their" instead of "her."

The third sentence is also incorrect:

3. Wonder Girls are doing the best to be a world star.

In this sentence, the definite article "the" before "best" is unnecessary. When talking about the best, we usually omit the definite article.