Unfortunately you can't just refuse to allow the car to be totaled if it meets the criteria to be totaled. More than likely you'll have to prove the value of the car is higher than the repair costs from the accident. Yes, you absolutely want to get enough money to fix the car, but it's a balancing act. If the repair cost exceeds the value of the car, the car usually gets totaled regardless of anyones wishes. At that point the insurance company will cut you a check for the value of the car. In some states you'll have a buyback option straight from the insurance company, in others it can sometimes be up to you to make the arrangements yourself. What you'll want to do in the meantime is gather evidence of the car's value, because more than likely the estimate that the insurance company uses will be LOW. Look up ads for similar cars for sale, not just 4 doors but 4 doors that are in similar condition. You can pull up completed sale ads on eBay, etc. That can help you establish the value of the car, so hopefully you can raise it enough that the car being totaled isn't an option that's on the table for the insurance company.
Not all of that is set in stone, it will depend on how you had the car insured and the rules regarding totals/salvage vehicles in your state. Some are friendlier than others as far as the process goes.
Just based on what I see in the picture, you may very well have to do some work to raise that value the insurance company is going to give for your car if you want to prevent it being totaled. Bumper and brackets, grille/headlight bezel, lower filler panel, hood, fender are all involved for sure. Cost for repair usually exceeds new parts for parts that are available because of labor costs, so even if there isn't any structural damage there could easily be a few thousand dollars worth of work there because not all of those parts can be bought new. Which may give you an uphill battle on not having it totaled out.
I would be working hard to find similar examples of that car with high price points. It looks like a nice, clean, original car, so that will help.