I am trying to find the existence of difference in achievement of boys and girls. I used Independent samples t-test but does it take care of the difference in skewness of the distribution of test scores. (There seem to be in my data)
This is a matter of degree. With important skewness, the test result may not be a good basis for a valid inference regarding your population. With important skewness, your mean will not represent an adequate central tendency. Take the example of wages. Generally, the mean wage of a country is distorted by a few very important salaries. This results in a mean salary for the population being higher than the median salary. For that reason, more robust indicators like the median are relevant when there is important skewness. Note that other solutions (transformation of scores) are also possible, but have their own drawbacks.
If you think that skewness is an issue, you may want to use a nonparametric rank-based test like the Mann-Whitney (for example). Under a non-normal (asymetric) distribution, the Mann-Whitney U test is generally more powerful than its parametric counterpart (t-test).