For a grassy ground cover, you can plant red fescue and don't mow it. One of the purposes of grass is to prevent rain drops from slamming into the ground at full speed.

For a non grassy ground cover you might look at Asiatic jasmine. It can take some time to establish, but once it does, you never have to water it.

build tiers so you can drape it in cascading plants.

There are several types of retaining wall from wood to block. I like retaining walls here in socal because it opens up the space. If u need a contractor in socal let me know and I can give u a referral depending on your area. I design landscapes but can refer to install crew if u need help. Also.. I like the idea of a vine on the wall to bring height to the area.

Trees and retaining wall: the infill soil material would suffocate the existing tree roots and the trees would die. Do you plan to keep the trees?

Good idea Jackie Bunao! I recommend that you read this Forever Green article for hillside decoration: “Hillside Landscaping Ideas for Commercial and Residential Areas”

When you re-landscape, remember that the dog will want to patrol the fence line. So don't plant up against the fence and leave that for the dog.

One of the right posts talked about NON-mowing grasses, and that might be something to look into.

I'd try this non-mow grass arrangement on a slope. The plants in this photo are

1. Artemesia arborescens
2. Achillea 'Moonshine'
3. Stipa tenuissima, and the red plant on the bottom left is
4 Escheveria 'After Glow, which you could do in a pot on the patio.

some ideas

Nice shade to sun transformation! I'd like to do that in parts of my yard.

What kind of trees are those?