Can I convince you to not do this ?
Honestly not trying to be an ass.
Please, please - Get a quote from a company that builds retaining walls.
The quote will cost very little or nothing.
You will be shocked at the cost, and not in a good way.
The quantity of material needed to build the wall, will amaze you.
Please get a quote or two first.
I promise you, you will not regret it.
Block walls work in compression, heavy things directly on top of them is fine.
Side to side, their goal in life is to tip over, and they are damn good at it.
Blocks work because they are tied to very solid, heavy things at the top and bottom that run the length of the wall, and have regular supports at a right angle to the length of the brick.
A 1' deep pile of soil, behind a 4' block wall, 1 block long, weighs 500 pounds.
The path of least resistance is to knock over the wall.
Blocks, attached with mortar, to the soil behind the wall about as strong as a 2x10 resting on its edge.
The question is more one of how many yards of concrete will you need to build the footing.
You can hold up 2' of dirt with wood structures. That's essentially what wood planter boxes are. But will it look good? Probably not...at least, not over time. Wood is flexible, gets wet, gets sun damaged, and the posts supporting it will suffer the same fate. If you don't care about looks, then it's probably OK, but if you want it to look OK over time, I'd suggest you consider retaining wall blocks or the like.
UPDATE:
Coming back to this as I think I answered before I saw the photo. I think you could probably make this work. However, I don't see a whole lot of space between the fence and the side of the house. Do you have a basement? If so, this slope is probably intentional to provide adequate surface run-off to keep your basement dry. Do you live in an area where you can get heavy rains at time? If so, I'd suggest not leveling this part of the yard.
Best Answer
The engineering on such a wall may prove difficult. We recently built a 6' retaining wall and a couple of 5' retaining walls. The 6' wall was 32 MPA concrete spray using our pool as the footing, the 5' walls are steel reinforced, core-filled besser blocks with footings 600mm deep and 1000m wide. In both cases, using steel and concrete, the engineering was complex. We rendered both walls. We constructed our walls this way to minimise the foot print (the walls are 200mm thick).
Using something like boulders could prove tricky unless you have a 45 degree angle of repose - this would simplify things but also eat up a lot of your back yard.
My neighbour has just build a shorter retaining wall with besser blocks then added a rock finish afterwards - looks rather nice.