Options for Landscaping Slopes
Let's deal with each of these in order
Hardscape
In order to create garden areas on a steep slope, the easiest way to do this is to create terraced areas. You build a solid retaining wall and excavate the soil to level to that wall. Go down the hill another few feet and build another retaining wall - excavate to backfill to level. In this way, you create what is essentially a large stairway down the slope.
You garden on the level areas in whatever manner you prefer.
Advantages: You get a lot of gardening space out of otherwise difficult terrain. You can easily work each bed.
Disadvantages: Building retaining walls can add significant costs to the project. If done over time, it may be worth investigating for gardeners on a budget.
Terraced Garden in the Shade
Turf
Many people imagine landscaping slopes will be easier than mowing up and down a hill. The reality check here is the answer is yes and no depending on which option you pick and how much time and money you want to invest in the landscape project
Turf is the least expensive option and not necessarily the most amount of work. Although hauling a lawn mower up and down a slope can be seen a rigorous exercise one doesn't have to pay a steep membership fee to achieve.
Option - buy a self-propelled lawn mower.
Ground Covers
There are ground covers for sun and shade that will fill in almost any area. There are two negatives to this scenario.
Cost - purchasing ground covers isn't necessarily cheap as you're going to require one plant for every square foot of slope.
Maintenance: This is one of the biggest myths in the gardening world that one lays down a ground cover and the work is done. The reality is that until the ground cover is established, you'll have to weed regularly by hand to pull out every bit of invading grass and spreading weed. Unless you do that, the grass will gain a foothold and will recolonize the area.
Ongoing maintenance - no ground cover is foolproof against grass invasion so you'll have to go in and hand pull weeds on an ongoing basis. Not as much time as the establishment period but yes, you'll still have to do it on an ongoing basis. Again, if you do not do this kind of garden maintenance, then weeds will establish themselves.
Evergreens
Combining evergreens with a weed fabric and mulch will reduce any landscape slope maintenance to near-zero with a twice yearly walk-through to pull any invading grass or weeds. Weeds will establish themselves in the mulch and can be difficult to pull out if the roots become entangled in the weed fabric.
Advantages: When mature this is a lovely looking project for landscaping slopes and works really well as a low labor system.
Disadvantage: It is costly to buy the shrubs and materials and a great deal of work to plant them all
This is the same issue for woody shrubs - lovely to look at but still expensive to purchase.
Grasses and Perennials
See the above discussion and remove the weed fabric. You can't plant perennials through weed fabric because the purpose of the perennial is to expand and fill all available spaces. Weed fabric would stop this.
So it's a gorgeous option but it's the same amount of weeding and work as having a large perennial border on the flat ground. Not so much when established but a lot to establish and it can be pricey depending on the plants.
Combinations of the Above
This is serious gardening at its best - with retaining walls and perhaps simply lawns laid down so you can still mow but on more of a level area than on the straight slope. Or retaining walls with full gardens on each level.
Yes, this is landscaping, not natural
Bottom Line
I have just this situation on my back lawn sloping down steeply enough that pulling a lawn mower is impossible. There's no soil there to set up a retaining wall situation so I'm currently mowing it (I own a 4-wheel drive lawn tractor) and will likely continue to do so.
Landscaping slopes is a compromise between cost and effort and it's this balancing act you're going to have to work out for yourself. I hope this article gives you some sense of your realistic options.