In the following sentence, why have author used "did have" instead of "had" ? Is it grammatically correct at all ?
I don't want to diminish her achievements, but she did have a lot of help.
Yes, it is correct. Did is used emphatically. Considering your case, the use of did have makes the sentence similar to
I don't want to diminish her achievements, but she had a lot of help indeed.
The following sentences are fine:
I warned Clara that it would be dangerous.
I did warn Clara that it would be dangerous.
The second one suggests that the speaker was right about warning Clara as something has probably happened to her.
Notice that you can use the same structure with the present simple (do/does + base form) :
She does know how to make people happy.
She really knows how to make people happy.
When we want to give a sentence positive emphasis in English, we normally put stress on the auxiliary verb (including the normal use of the verb BE). The second examples in the sentences below are emphatic. The stressed words are in bold italics:
Notice that if we want to stress the auxiliary, we cannot contract it. For example in the first emphatic sentence we see "She is", not "she's".
Sometimes we have a small problem, because some sentences in English do not have an auxiliary verb. We don't usually see an auxiliary verb in normal sentences if we use Present Simple or Past Simple verb forms:
When we want to make these sentences emphatic, we need to use the dummy auxiliary verb DO. This is the same auxiliary we use to make negatives and questions in the present simple and past simple:
Questions
Negatives
Emphatic sentences
In the emphatic sentences we see the dummy auxiliary DO being used so that it can take stress.
The original Poster's example
I don't want to diminish her achievements, but she did have a lot of help.
That last clause is an emphatic version of:
DO is being used as a dummy auxiliary here.
Hope this is helpful!
do
. Googling gave me this page which has a couple of easy-to-understand examples