Due to no insurance accident is there a way I can get my license back without having to pay total amount of Judgement?

You certainly do NOT have to agree to a $26,000 payment plan, and you certainly should not even think of doing so, or borrowing from your friends and family, without some good legal advice you can rely on. That would take a local Florida lawyer you retain to advise you, and I am not a Florida lawyer.

What seems to have happened is that the other driver's insurance company sued you -- just as the other driver and any other insured person could have -- under the subrogation provisions of its insurance policy with its insured. When you missed the court date the other driver's insurance company entered a default judgment against you for $26,000. (By the way shame on you for letting that happen and double shame on you for not having had insurance.) You should have seen a lawyer way before this and it would have been a lot easier to and less expensive to deal with.

How did the judgment come up to $26,000? Presumably the other driver's insurance company paid its insured and any passengers for the injuries sustained in the accident under the uninsured motorists portion of its policy, plus its insured's costs for repairing the car, a rental car, etc.  To those hard dollar figures the other driver's insurance company probably added some claimed costs in handling the matter (and experience suggests such costs were possibly extraordinarily over-inflated) and possibly interest, lawyer fees and court costs.

When you failed to show up it presented the costs to the court, no one was there to argue that they were too high, and the court entered judgment. (Had you hired a lawyer earlier it never would have gotten that high.)

It also appears that your state may have a law that suspends the driver's license of any person who drove while uninsured and fails to pay the judgment against him. (I am just surmising.)

Depending on how the other driver's insurance company happened to get a judgment you may be able to have the judgment nullified (such as if they failed to serve you with process, or they failed to send you the required notice of the hearing) or negotiated way down.

How will the lawyer negotiate it way down? If you have a lawyer and the lawyer says to the insurance company unless they consent to a much lower amount s/he will seek to have the judgment vacated, and even if that approach is not successful you will declare bankruptcy in which you will wipe the $26,000 judgment in full. That gives the other driver's insurance company, known as the judgment creditor, a choice of taking what can be negotiated and reducing the judgment -- perhaps for $2,600 in cash or $3,000 over 12 months -- or take the risk getting nothing if you file bankruptcy.

Once you complete bankruptcy you'd likely no longer have an unsatisfied judgment so you may get the license back. Again, that takes a Florida bankruptcy lawyer to know, and I am not a Florida lawyer,

No matter how smart you are, as a practical matter you can not successfully do that on your own or get as good a deal as a qualified lawyer can get you. The lawyer will charge for his or her time but certainly would be able to avoid financial ruin and bankruptcy and loss of a license and you'll be way ahead.