how to patch the wall with multiple layers of paints?
First, make sure any loose or chipping paint is removed.
Second, for an area that large, I would use joint compound instead of spackle. Also, a wide taping knife will help.  

One more tip: For a relatively small area such as this in an existing house, in order not to get so much dust in your house, I recommend the following:  


Be careful not to apply too much joint compound. Use your knife to eliminate ridges when you apply it.
After the joint compound dries, use the damp sponge "sanding" method to smooth what imperfections remain. After this, actual sanding may not even be necessary.