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There's not an example out there, but you'll do well if you'll explain it to the IRS like you're explaining it here.

Here's the IRS' guidance for Box 7 in the Instructions for Form 843: 

If you are claiming a refund of excess social security, Medicare, or RRTA tax withheld by one employer, you must, if possible, attach a statement from the employer. The statement should indicate the following.

• The amount, if any, the employer has repaid or reimbursed you for excess taxes withheld.
• The amount, if any, of credit or refund claimed by the employer or authorized by you to be claimed by the employer.

The employer should include in the statement the fact that it is made in support of your claim for refund of employee tax paid by the employer to the IRS.

If you cannot obtain a statement from the employer, you should attach a statement with the same information to the best of your knowledge and belief and include in the statement an explanation of why you could not obtain a statement from the employer. Attach a copy of your Form W-2 to prove the amount of social security, Medicare, or RRTA tax withheld.

First, speak to the bulleted points above, including an explanation of why FICA shouldn't have been withheld (or was over-withheld), and then address your efforts to obtain the employer's statement. You don't need to write a novel, just lay out the facts and the efforts you've made to resolve the issue. 

You'll notice that Box 7 of Form 843, Claim for Refund and Request for Abatement doesn't give you an awful lot of space.  The form in the link is fillable; feel free to begin typing your statement into Box 7 and then type "See attached" when you've run out of room, attaching the remainder of your statement.

You state that this is your first time filing a return, but don't mention whether you're a non-resident.  If you are, in fact, a non-resident, please see Refund of Taxes Withheld in Error on the IRS's Social Security Tax / Medicare Tax and Self-Employment page for more relevant information.