The idiom is "don't go all [noun/adjective] on me". It's an expression of dismay at the other person's behaviour - or, more precisely, the future behaviour that the speaker thinks might occur if they don't prevent it.
For example:
Is there anything about your house that, you know, kind of...freaks you out?
I just decided that for me, it's our dishwasher. It sings.
Now, don't go all Nancy Drew on me and decide to investigate this the next time you are at my house, because I'm pretty much positive that it will NOT sing when you want it to.
By "don't go all Nancy Drew on me", the writer means, "please don't actually investigate this". They thought that the reader might, after the previous paragraph, decide to investigate the dishwasher, and said "don't go all Nancy Drew on me" to mean:
- if you do this, you'll be behaving like Nancy Drew (this is probably irony and/or exaggeration) and
- I don't want you to do this
Another example:
She sighed, exhaling fifty years of dusty excuses that were a bit feeble even when she made them up. She picked up her knitting and started clicking the needles ferociously. 'I didn't go abroad again because there wasn't any point. Spain had been a silly teenage adventure. I accomplished nothing. Got my fingers well and truly burned. So I learned from my mistakes and stayed here.'
'But what did you accomplish by not going away again?'
'I made a life here. Are you saying that teaching accomplishes nothing?'
'Don't go all defensive on me, Mum. I'm trying to understand you. You were a brilliant teacher. Everybody says so.'
In this instance the daughter says, "Don't go all defensive on me" because
- she thinks her mother is starting to become defensive from the line of questioning
- she thinks her mother will become more defensive, or at least continue to be defensive
- she doesn't want her mother to be so defensive
Usage
I wrote [noun/adjective] at the top, but the truth is this is usually used with an adjective.
e.g.
- Don't go all broody on me
- Don't go all paranoid on me
- Don't go all melodramatic on me
- Don't go all dreamy on me
- Don't go all geeky on me
Because the phrase as a whole is describing a type of behaviour, it can only be used with a noun when there's a certain type of behaviour associated with that noun. This could be a famous person (fictional or not) who is well-known for having a certain type of behaviour, or a stereotype of a certain type of person.
e.g.
Some of these will not have a clear meaning from the sentence alone. The Boy Scout one is an obvious example of this - there are certain traits that could be inferred (for example over-preparedness) but you would need context to know for sure which trait was being criticized.
Your example
In your example, "Don't go all shaky on me" means,
- Jack is concerned Bob may physically shake.
- He doesn't want him to.
Bob may have started shaking, and Jack wants him to stop, or perhaps Bob hasn't started shaking yet, but Jack thinks that he will.
Since Bob is a toy, this is probably a sort of hope/prayer that's being spoken to Bob but not really directed at him - Jack is either talking to the machine as a whole, or hoping his own piloting will be steady enough that Bob doesn't shake.
