Nasty retaining wall outdoors needs an enduring decor- concrete Paint perhaps ?
Sarah...Glidden says they have concrete paint that stands up to what life throws at it and cost is less! Might check it out!
The most durable exterior paint is going to be an epoxy or good exterior enamel or even ones for garage floors. Check with your home store to see what they have. There are also some marine paints that are excellent (but costly). If you don't really need to paint the entire wall in the super-paint, you might want to fashion a design of some kind and use a regular type exterior paint starting 1/3 to 1/2 way up. It could be just what the wall needs for a new "life". Cheers!
You may wish to research how people feel about exterior concrete they've painted before deciding to do this. My HOA requires that we paint our concrete driveways and while they look quite nice for about 2 weeks, the weather takes a toll almost immediately. This requires repainting every 1-3 years!
Now, you may not have such extreme issues as this is a vertical area and cars won't park on it but....check it out with others first.
Alternatively, consider planting trailing flowers above the wall, applying tile to the wall and/or hanging art on the wall rather than painting.
Now that that's covered, I did recently read and watch youtube pieces about "properly" painting concrete. The trick is supposedly to (after thoroughly cleaning, prepping, drying using KrudKutter concrete wash and etch) wet down the bare concrete, keeping a spray bottle handy. Use latex paint watered way down and put an initial wash on the concrete. As concrete is porous, this wash is supposed to sink into the material rather than just laying on top. If your concrete dries out while you're working, spray more water.
After this wash, return and paint with latex exterior paint until the surface is properly covered (you'll have to see how many coats but 2, possibly 3). Then put a sealer on top to make it weatherproof. The best color sealer outdoors will be a Marine varnish.
Mix in a small amount of concrete powder with the paint. Make sure there is no flaky paint on the wall- give it a good scrub.
SPRAY WITH MOLD mildew remover then pressure wash..apply KILZ primer then use concrete paint and later apply a concrete sealer