Shall i complain to ombudsman/irdai or issue a legal notice?

Yes.  You have to complain to file at Ombudsman, IRDAI and if they do not respond, approach the Consumer Redressal Forum.

If the requested documents are relevant then it becomes your duty to comply with the requirements for settlement of claims.

You cannot decide about the documents to be submitted, the insurance company will go by their prescribed procedures hence any complaint to the insurance ombudsman will not fetch you the desired reliefs.

You may first of all decide what can be done to produce the documents as  instructed by insurer and the source to obtain them.

Your vexatious mind cannot support your claim hence first exhaust the remedies available before you, before you plan to initiate legal action against the insurance company for deficiency in service.

You may provide the documents that are available before taking up the issue with the ombudsman or approaching the consumer or judicial forum.

If you had provided all documents relevant to the claim, the insurer shall not demand any other document, which is irrelevant to the case.

Consult a local prudent lawyer for proper appreciation of facts / documents, professional advise and necessary proceeding before competent Consumer Disputes Redressal Commission.

It is not on you to decide whether the documents are suffiecient for the insurer to grant you the claim, you should submit all the necessarydocuments, i belive that succession certificate would also be required which you have to obtain from the court. 
Kindly fulfill the documents which are requested before you and before taking any legal action agaisn such an issue kindly follow the hierchial complain of the insurer complaint.
Litigation would be of no use if the they raise the request of same documents in thier reply before the court. 

Don't waste your time at Ombudsman. Send complaint to IRDA, through online portal. If Insurance company resolves your complaint then the matter gets a closure. If not, file consumer complaint before District Consumer Commission.

Dear Sir/Ma'am

First of all, sorry for the delayed reply. The delay happened due to some unforeseen circumstances.

Secondly, I was confident that I have furnished all the necessary documents & those documents were more than enough to process the claim. From Post Mortem report to the ACP's closure report, I produced strongest pieces of documentary evidence which clearly prove that the death was accidental. I was pretty sure that the company was making unreasonable & even invalid demands, just to make me lose the hope & give up (This company is quite infamous for their claim settlement) and looks like I was right as they have finally accepted thier defeat & have responded to my e-mails stating that they are ready to pay the entire claim amount. They have couriered me a discharge voucher, requesting to sign & return it. But I want additional compensation for the mental agony I had to suffer from, due to the insurer's unreasonable, unwarranted & even invalid demands. So,

1. What options I have to claim the same?
2. Is it worth going for it (Considering the time & efforts it would take) or it would be better to accept the insurer's offer?
3. Is there any risk (Like the judgement being passed in the insurer's favour & instead of getting any additional compensation, I receive amount lesser than what I would have received otherwise)?
4. How much additional compensation one usually gets in such cases?

Kindly guide. Thanks in advance.

The additional compensation is not part of the insurance claim, hence you first get the claim amount paid after which you can think over it patiently and decide if it would be worth enough to pursue the additional claim towards the mental agony and harassment you faced.

If the insurance company has decided to settle your claim in full, then it is not worth to file any case seeking additional compensation. In India, the Courts are mostly reluctant to grant significant amount for general damages. 

The time, effort and cost of pursuing any additional compensation is futile in country like Republic of India.

Sir @T. Kalaiselvan

Thanks for replying. 

Though I haven't received the discharge voucher yet (Have received only an e-mail stating that they have couriered me the voucher, asking me to return the same by signing it), I believe that they would have mentioned in the voucher that the amount they are compensating with, will be the full & final payment from their end. Signing the document will mean that I am agreeing with the settlement amount. 

So can I still claim for additional compensation after signing & submitting such a document?

Yes, first you receive the amount by sending back the voucher duly signed after which you can start legal proceedings to claim compensation for the period of delay.

Proceed as advised by learned senior expert Mr. T Klaiselvan, which I endorse.