This essay has already been corrected in a few other Internet forums, but here goes anyway!
Your introduction sentence is a little general:
A lot of scientists claim that genes and the environment play a significant role in shaping people's character.
What else could shape character, if not genes or the environment? Perhaps it would be better to give both sides in the introduction:
Are people the product of their environments and experiences, or are their characters decided before birth by their genes?
You don't have a thesis sentence, so I'm not sure from reading the introduction what your essay is going to do. You also haven't given your opinion - that's optional but it's often safer to give it in the introduction in case your essay doesn't turn out as planned when you are writing it. The official IELTS descriptors for Task 2 stress the importance of a clear position (see under 'Task Response').
The most confusing part of this essay is Paragraph 3. It starts with a good topic sentence:
Let's consider cases which clearly demonstrate the link between the environment and character
But then there are some sentences about identical twins having the same preferences even though raised apart. This would seem to be in favor of genetics. Then the paragraph goes back to the idea of twins who were raised apart having different characters - one outgoing, one introverted. Would it help if you left out the part about sharing, or reorganized the essay?
Word Choice and Usage, Articles, other grammar points
- One of the twin ==> One of the twins...
- Countryside twin is unflappable ==> The country twin was unflappable...
- All these arguments lead the the conclusion ==> All these arguments lead to the conclusion...
- That's why, no doubt that influence of the environment and nurture is more obvious ==>
- That is why there is no doubt that the influence of the environment is more obvious (OR)
Without doubt/Undoubtedly, the influence of the environment is more obvious.
- Indeed, the influence of nurturing is so overwhelming and powerful that's why criminologists state criminals are often the result of bad parenting or bad nurturing ==>
- Indeed, the influence of nurturing is so overwhelming and powerful that criminologists state criminals are often the result of bad parenting or bad nurturing.
In paragraph two, you change from present to past back to present. Stay in one tense, if possible.
Paragraphing: the reason for your paragraphs is not always clear. Perhaps the 4th and 5th should be together.
Be careful not to introduce new material in your conclusion. You finish with the example of criminals and parenting - this could have been discussed earlier.
All in all, there are some excellent ideas, sentences and vocabulary here, but some reorganization is needed to make your ideas clearer.