The Plan For A Clearly Guilty Client Without Bargaining Power
This question underestimates how much of a criminal defense lawyer's work involves sentencing rather than a determination of guilt or innocence.
Suppose as the OP does that the prosecution can easily prove beyond a reasonable doubt that your client is guilty, you client has no plausible defenses, and the prosecutor won't budge on a plea.
As a criminal defense lawyer, you may well advise your client that there is no percentage in fighting guilt on the charges, and have your client plea guilty. This prevents the prosecutor from spelling out for many hours in excruciating detail exactly why your client is guilty and the harm the resulted from the crime, which could harden the judge in the sentencing phase. It also frees up a client's often scarce resources for legal work that is likely to be more fruitful and for things like paying fees associated with alternative sentencing programs and paying restitution.
It is an empirical fact that judges sentence criminal defendants who plea guilty, even in the absence of a plea bargain, less harshly on average, than criminal defendants who insist on going to trial. (When there is a plea bargain "sentences following convictions at trial are five times larger than sentences received by those who plead guilty".) Often the sentencing premium for going to trial is stunningly large to the point where it has been argued that it amounts to an unconstitutional burden imposed upon the right to a jury trial.
Then, you focus entirely on the sentencing phase of the case.
There's More Discretion In Sentencing Than Guilt Verdicts
Short of first degree murder and a handful of other crimes, there is almost always some discretion on the part of the judge regarding the sentence to be imposed, no matter how clearly guilt is established.
Often a judge has the power to sentence someone guilty of a minor felony to probation or a "boot camp" or "community corrections" or even a fine without incarceration, rather than a prison term. Often a judge has a wide range of possible lengths of incarceration (especially in misdemeanor cases and for very serious felonies).
Often the corrections department has considerable discretion over which facility to commit a client to and some are better than others. So paying attention to the facility assignment process also matters.
Where a defendant is facing both state and federal criminal charges, it sometimes makes sense when conviction on all charges is likely, to plea guilty immediately to the federal charges so that the defendant is already in federal prison before pleading guilty to or going to trial on the state charges, so that if the defendant is sentenced to serve time for the state and federal charges concurrently because they arose from the same incident, the time is spent in the more pleasant federal prison rather than the less pleasant state prison. (This is the case because violent crimes are overwhelmingly prosecuted under state law, while a large share of federal crimes are white collar or are for immigration and non-violent drug offenses. So, your fellow inmates tend to be less vicious in federal prison.) Not infrequently, state prosecutors will even drop state charges to conserve their scarce resources, if they know that the defendant is already facing a significant term of incarceration following a conviction on federal charges.
A criminal defense lawyer thus almost always has something to argue at sentencing because there is almost never only one possible result of a sentencing hearing, even if all of the facts are not in any dispute whatsoever. The judge's interpretation of what those facts should imply in terms of a sentence is always up for debate and argument.
What Do Lawyers Do In The Sentencing Phase?
As a criminal defense attorney in a case like this, your job is:
to present your client in the best light possible,
to locate witnesses who will testify that he has support in the community and that he is basically a good guy despite this particular lapse,
to marshal testimony that extended incarceration will be a hardship to someone dependent on him,
to have him sincerely apologize to the victim and try to do something immediately to make it up to the victim and to show regret and contrition,
to support him in not violating terms of pre-sentencing release if any, and
perhaps even to see if charges that might otherwise bring him into a recidivist sentencing regime can be sealed or vacated for any reason.
You present mitigating evidence regarding IQ or mental health conditions or prior military service or poverty or provocation that explain your client's conduct, even if it doesn't excuse it.
You try to get the prosecutor to agree that a harsh sentence isn't necessary here, or even to support an alternative sentencing option. Prosecutors are frequently more sensitive to their win-loss record of securing convictions than to precisely how the people they convict are punished.
You scrutinize the pre-sentencing report for any inaccuracies and prepare to prove that they are inaccurate.
You litigate which category your client belongs in under the sentencing guidelines that apply, if any, which are often the subject of much less case law and hence afford for more room for interpretation.
For example, in a recent case handled by another lawyer in my office (I don't do criminal work myself, but have colleagues who do), the client's sentence was reduced by more than 95% from what the prosecution requested because they had meant to charge 300 counts of a municipal ordinance violation for which each day counted as a violation, but actually charged our client with only 2 counts of the municipal ordinance violation, and the judge held the prosecution at sentencing to only a sentence based upon the offense actually charged in the relevant documents.
You prepare to explain to the appropriate people how maintaining community ties through visitation will reduce his odds of recidivism if he is located at a more favored correctional facility rather than a less favorable one.
You prepare to explain to the appropriate people that your client's survival would be a risk based upon the gangs present at a less favored correctional facility, or that he would be more likely to join a gang and thus commit more crimes upon release at a less favored correctional facility.
You get your client to be cooperative in paying any restitution he can afford to pay even before the court orders him to do so.
You find decent clothes for him to wear to his sentencing so he doesn't look like a thug and teach him what not to say at sentencing that would piss off the judge. You have him do his hair in a way that makes him look as vulnerable and inoffensive as possible. You have him cover his tattoos and remove his piercings as much as possible.
If your client is black, you find a white or Asian-American relative or mentor or girlfriend or supporter to stand at his side and support him in court. This shouldn't matter, but it almost always does.
If your client doesn't speak English well, you find a relative or mentor or girlfriend or supporter to testify in fluent English in support of leniency and make sure that there is an interpreter lined up for his sentencing hearing.
You remind the judge of other more serious cases involving the same offense to which your client's can be compared, or of the sentences imposed on more culpable co-defendants, to suggest that your client's sentence should be less severe.
You downplay the harm caused and emphasize your client's future prospects.
You help the judge relate to your client anyway that you can. You may need to research the judge's background and history of sentencing decisions to find out what this particular judge does or does not find persuasive in sentencing hearings.
Sentencing Is As Important As The Charge Of Conviction
A criminal defense attorney who presents a solid sentencing case may leave the client who receives a near minimal sentence on that charge with a lighter sentence than one who plea bargains to a lesser charge but then botches the sentencing phase resulting in the client getting a near maximal sentence on the lesser charge.
Consider, for example, the attorney who represented Brock Turner, a Stanford student convicted of raping an unconscious woman in public in the face of overwhelming evidence against him who, nonetheless, was sentenced to just six months of incarceration (reduced further for good behavior in jail). Another attorney could have plea bargained down to simple assault and still left his client with a more harsh sentence. Turner's attorney was so effective in securing a lenient sentence that the sentencing judge was recalled for the first time in 87 years in California for his leniency.
So, the notion that a good criminal defense attorney's job is over when the client has no chance of establishing his innocence is just fundamentally wrong. Roughly 90% of criminal defendants will plead guilty and half of the rest will be convicted. The vast majority of these criminal defendants are guilty of something, even if not the exact offense of conviction.
The criminal defense attorneys' job isn't mostly about getting acquittals for clients who are, the vast majority of the time, guilty of something, it is about securing a non-excessive sentence for the conduct committed.
Even in most cases that go to trial instead of concluding with a plea bargain, most of the job is about the sentencing phase, where there is almost always more judicial discretion, and not about the guilt-innocence phase of the case.