It isn't unusual to have to remove some stuff to get the battery out, though it is unusual to have to remove the air cleaner. You have to do what you have to do, it is mostly an intuitive process.

I advise you to ensure you are well-informed about working with batteries safely regarding acid, explosive gas, accidental sparks and short circuits and the weight of the battery.

They can be dangerous - they can explode if not treated with proper respect.