Building raised garden beds on a slope is simple with a bit of digging. Setup your raised beds so the long sides run parallel to the slope and dig into the hillside (rather than build out) to create a firm foundation below planters.
Don’t worry about leveling the entire area, just make a trench where the planter sides will be placed and level the boards as you go. A carpenter’s level will come in handy. Plant ground cover or use stone work to prevent erosion on steep slopes.