They say there are five stages of grief...
Leonardo will blame himself for it no matter how you die. Did you get sick? He's a ninja. He should have noticed the symptoms as soon as they appeared! Did the Shredder kill you? God, that's his worst nightmare. Because it not only means he failed as a partner, but he also failed as the leader of the team you belonged to. He couldn't protect you, and he can never forgive himself for that.
- Denial
There must be some way to rebound it. His mind flashes from here to there, and Leo considers possibilities that in a normal situation would seem delusional. Could Donatello build a time machine? There must be some way to reverse it. There must be. It can't be that you're just... gone.
It's a sheer tough situation because even though he would want to fight recklessly, with no regard for himself, Leo has to be strong for others and continue playing his role as leader and older brother. So he bottles up his feelings; buries them deep until they slowly rot inside him.
When he faces the Shredder again, he notices that there is something different, and for the first time in decades, Shredder fears he may not win. I think Leo would also become rougher with low-ranked criminals, hitting harder than necessary. The terrifying part? It's always perfectly calculated.
Also, his brothers resent his anger during training because he becomes tougher and more demanding. However, it's only because Leo can't afford to lose anyone else. He wouldn't be able to bear it.
He should at least be able to compensate your family. Friends. Anyone who loved you as much as he did. Thinking about doing things for people who were close to you brings him a kind of comfort that appeases his anger. It's a way of trying to regain a sense of control over the situation and find a way to cope with his pain.
He'll never again feel the tender caress of your fingertips over his shell, the warmth of your lips pressed against his own, or the sweet melody of your laughter echoing through the lair. The realization grips his heart with an ironclad vice, suffusing his spirit. It's a devastating blow that rends his very soul asunder.
But you wouldn't want him to be sad forever. No, in fact, Leo is sure you'd be insisting that he needs to move on. It was okay to feel, to be upset and cry along the way, but it was time to get up. Master Splinter plays a very important role in how Leo slowly recovers himself. One step at a time.
Donatello: It depends on how you die, but I believe what could drive him insane is if he loses you slowly due to an illness. That would be his personal hell because no matter how hard he tries to change things, researching new methods, creating medications, even biotechnology... nothing seems to yield results. Isn't he supposed to be a genius? What's the point of intellect if it can't use it to save you?!
- Denial
"With this cryogenic capsule, I can keep her body intact a little longer," he tells your loved ones, who stare at him, paralyzed by the desperation in his eyes. "I can fix this. I can- I just need more time." But a person is not a machine, and your loved ones did not allow him to experiment.
A machine! That's it! Donatello made a copy of your memory and some parts of your consciousness before your departure; perhaps he could put that into a robot and somehow... maybe with enough effort and the right wires...
It worked, and yet it failed miserably. This thing in front of him looked like you, sounded like you, shared some memories, and yet, it felt utterly empty. How could he insult your memory out of his own desperation?
Donatello smashed his Bo staff into the control center, piercing it completely. He trembled a little as he continued to hold it, buried in the circuits. That night there was a blackout in the lair, and all that could be heard from the lab was the grinding of teeth.
It happened to you, but perhaps with all the research and testing, Donatello could prevent someone else from going through the same thing. So, he decided to sell his investigation, using a pseudonym and a couple of computer skills made it no problem to do it all from the lair. For him, it's like gradually adapting to the reality of his loss through these small actions.
To think that a robot could replace you. What the hell was he thinking? Your scent, the softness of your skin, the beautiful way you looked at him when discussing a new discovery, that could never be replicated. The lab, like his heart, felt terribly empty. It was a feeling as suffocating as it was overwhelming: knowing that you would never be there again, that he couldn't see or hear you anymore. Suddenly, he can't breathe.
Burying himself in his work keeps his mind occupied. He doesn't need sleep; he needs to progress with the research. Donatello escapes from every little space that could allow you to somehow appear in his mind.
April helped a lot in this part, as she was the one who started bringing you into the conversation with positive things, and Don has small spaces to feel shared nostalgia. April feels the same loss; she understands, and that is extremely comforting.
Over time, the feeling of emptiness left by your memory transitions to a bittersweet sensation, and gradually he allows himself to move forward, remembering you with a smile, with a fondness that embraces him from the bottom of his heart. Donatello learned that every minute counts, and for that reason, he now makes space to spend more time with the people he loves, and who love him in return.