Ranking higher on Amazon is mainly based on 2 factors: Relevance & Performance
Secure Relevance with Keywords
Every ranking optimization starts off with solid keyword research, which makes sure Amazon considers your product to be relevant for the specific search query. This is, however, only the basic foundation of every optimization.
Increase Performance with Sales - Use PPC to Score First Sales
To actually Increase your Rankings for all relevant searchterms, sales must first be made via these searchterms. As this is especially difficult when ranking on the back pages of the searchresults, other ways must be found to break the Devil's Circle.
The most frequent tactic for this purpose is the use of Sponsored Products (PPC), which will catapult your products to the front pages. Sales achieved via PPC will in turn improve your organic rankings.
Pro Tipp: Products in "Exact" Campagins are prioritized by Amazon and are more likely to be shown to customers. If you know the keyword is important and working for your product, you should therefore only add it to your exact campagin, while putting it on a negative keyword list in your other campagins.
Content Optimization First, PPC Second
It must be stressed though that PPC will only really work out for you if your product's content really is optimized, meaning optimal titles, images, bulletpoints and price, among other things. Otherwise your PPC campaigns will simply run out empty, be it by not attracting any clicks, or worse, receive clicks but no sales.
How to go about for your Content Optimization is described in more detail here!