We can say

as big as....

but is it right to say

as bigger as or He wanted to do it as better as possible.

What is the right way to say this thought?
You can't say "bigger" or "better" because what you have here is the comparative of equality which is formed by placing "as" before and after the adjective:

... as big as...
... as good as... / ... as well as...
So how shall i say?
Students: We have free audio pronunciation exercises.
Say 'He wanted to do it as well as possible.'