Depends on how high the wall needs to be. If it's less than 3 feet, probably cheaper to build one of the modular block walls that are free standing. Bigger than that, probably cheaper to grade the land. It's hard to imagine a 10 foot wall would be more expensive and invasive than doing the whole yard, however.
What's wrong with a slope? They're good for directing water away from the house. If you don't want a steep slope why don't you just bring in a couple of guys with shovels and a load of topsoil to reduce it to a more gradual slope. Should be cheap, quick,and keeps good drainage away from your foundation.
The 2 feet upward slope (which is 2 ft away from back of house & backdoor) is causing the water/mud from backyard to come toward the house; I have a french drain that's suppose to drain water but not the mud. Now the mud has covered up right against the door and over the rocks covering the drain.
see a pic here; this was before the mud covering up the rocks and tiles against the backdoor.
Get a skip loader or backhoe and re-grade. Should be around 800-1000 (ie 4 hrs ar 120 + 300 transport, or 8 hrs at 100 + 200 transport), more cleaner works. Two guys and a low-boy is almost the same costs but you'll end up with shovel marks all-over and uncompacted diet. Be nice to the owner operator and just tell them you only have a budget of 800 and if they can work with it. Frankly that's a 4 hr job or less. I've used a bobcat to grade 25ksf and it only took 2 days a little less maybe, but that's just rough grade.
Hi, I already had a retaining wall put in for a 2 ft tall retaining wall for $500, 8 ft by 2 ft and the landscaper guy removed most of the extra dirt that was laying around near the backdoor. I think how that much dirt in the backyard came from excavating/leveling the home for new piers and beams last year. Instead of removing the dirt, they planted it around the backyard. Lazy people!