Moving between 3-6 on similar keywords

So there are some very important keywords i need to rank well on. My competitors and I are swapping places daily, and I'm wondering if there's something I can do to stay top. Imo I have got the title and meta data as good as it can be.

My competitor's sites are much more authoritative than mine in that they are a decade old, but the specific page on mine is the only one that is actually relevant as the.