How do I write an analytical or personal response to 'What is the role self-preservation plays in a difficult situation?'?

The first issue here is choosing an appropriate text to which to respond. The assignment sheet does not specify any specific texts, and so the focus of this answer will be on a text that might work well for you. 

The first text I would choose for this is the short story "Shooting an Elephant" by George Orwell. In this story, the protagonist faces a moral dilemma. He really doesn't want to kill the elephant, but fears causing a riot or looking bad from a career point of view if he doesn't. There is some real tension here between his own moral beliefs and his need not to show weakness, which is necessary to succeed in his work and build a relationship with the native populace as a member of the British police force. 

For a hybrid analytical/personal essay, you should focus not on the specific events of the narrative, but on the moral issues it raises. Next, to turn this into a personal/analytical hybrid, you should compare this to some sort of dilemma you have experienced in your job or your studies. Think of a situation in which you have felt one course of action is right, but didn't take that action because it might have been risky, such as not standing up to a school bully or carrying out what you thought was a bad order from a boss.