How to repaint a wall with peeling paint
You only need to remove loose or peeling paint - you can paint over paint that is in good condition. Mechanical means (sanding or scraping) are typically sufficient to remove paint that needs to be removed.

In painting a single wall, you will likely have problems matching the color of the other walls. You'll be amazed just how many shades of "white" there are, and how glaring the difference can be. Depending on the use of the area this may not be a concern.

But, if you have water damage, you need to first solve the leak (source of water), and you may need to replace some drywall as well as (before) the painting to fully resolve the damage.