Do you always go for low hanging fruits first?

That's a pretty broad question. What sort of context are you asking about?

For example, if I'm starting a new development project or task, I will solve the difficult problem first in order to reduce risk early.

On the other hand, "low hanging fruit" generally means "things of value that are easily obtained" and therefore would usually be what you'd do first unless there's some reason not to.

On a personal level, there may be opportunity for growth and development for avoiding the easy wins and doing something more challenging.