You do not need to use PROMOTIONS option on Walmart to discount your product. Reduced price is the simplest way to offer a discount on your products.
1. Make sure your product is live. You can submit Reduced Price value only for products which are published already.
2. Edit a product, you will find Reduced Price value in the top section of the product page.
3. Submit your product (Save and Export to Walmart).
4. If a feed you submitted is correctly processed, within few hours your product will have a reduced priced shown:
This is how reduced price looks like on Walmart.com list of products page:
This is how reduced price looks on Walmart.com product details page (buy box):