I've been an auto mechanic all my adult life. I've been involved in engine repair right down to the empty/bare engine block. I also have extreme experience with the diagnosis and repair of electrical systems, including the removal and replacement of a simple part such as an alternator. A 5-10 minute job in the old days, longer on some of today's cars.
I've also had experience in court, mostly unrelated to auto repair, but I have been involved in complaints AGAINST mechanics, where I was the plaintiff. To win in court you need a logical description of the problem, plus proof. That means evidence. Material evidence, such as photographs or documents, like receipts. Then sworn testimony which is directly related to the complaint.
You have made your complaint here, which is clear. The mechanic changed your alternator. Your claim is that the mechanic caused the destruction of your engine "by not bleeding the coolent after he replaced my alternator". I can not think of a single car or truck or boat or industrial machine that required ANY contact with the cooling system. And technically, coolant is not bled from a cooling system, AIR is. Maybe you meant that the cooling system was not bled. But the words you use are very important. You did say "air pocket". But you need to say: did not bleed the air pocket, or did not bleed the cooling system, or did not bleed the air from the cooling system. But please explain how an air pocket came to exist in your cooling system, as a direct result of an alternator being removed and replaced. It's possible that some newer vehicle may exist that an alternator can not be removed without removing a coolant hose. I'm just not familiar with such an application. So please identify it.
Further you said this air pocket caused your engine to "overheat all the way to the red". This is the part that will need your explanation why you kept driving your vehicle once it showed signs of overheating. While it may be possible that the mechanic caused the conditions for your motor to overheat, you have caused the destruction of the engine by continuing to drive it once it was overheated "all the way to the red". If you CAN relate the changing of the alternator to the overhearing of the engine, you will lose your case because you didn't stop driving the car immediately, and have your car towed to the mechanic.
MY question, is how is the changing of your alternator related to the cooling system? You say that you have proof. Give us the proof.
If this story of yours was about the replacement of a thermostat or water pump or radiator or coolant hose, surely it would relate to the mechanic being negligent, but an alternator???
What year, brand and model is your car?
p.s. Because of a comment by MeBrod, I went searching and found that 1998-2000 Cadillac has a water cooled alternator, and a BMW has a water cooled alternator.
Please identify your car for us.