You can not control the movement in SERPS. That's basically called "dancing" and it happens to EVERYONE.
As for better ranking, the solution is almost always better rankings. That is assuming your onsite SEO is near perfect.
Links work in two basic ways: Authority and Relevance.
Authority links will be those with high Trustflow (read up on ratio compared to citation flow too). Google PR is dead. IMO (and many others), Trustflow is the most reliable metric today. No it's not perfect and sure it can be manipulated, but of all the readily available metrics, it is definitely the most reliable currently. HIGH TF links regardless of the subject matter WILL pass authority along to your site. Think Homepage Sape Links with your brand or site name as the anchor.
Relevant links are going to be those like from a PBN where the entire post is related to whatever subject matter the link points too. If your site is about outdoor tools, you want CONTEXTUAL links pointing at your site from articles/blog posts about grass cutting, weed eating, chainsaws, etc...All depends on your niche and kwds of course.
Then you can look at different tiers as well, meaning how many authority links do you point at the tier 1 authority links and so on. ALL depends on how competitive the kwds are that you are trying to rank for. And there is no "formula" to tell you. The more you do it, the more you learn as to exactly "what" you'll need to rank towards the top of page 1.
Hint: It's easy as pie to rank for many longtail (i mean LOOOOOOOONGTAIL) words, meaning you don't need a ton of links at all other than a handful of authority and relevant links if you flow the juice right through the site. Very small traffic though for each ind. kwd. So it becomes quantity. Many ways to skin the cat though.
It's ALL trial and error. Push until you rank something and learn learn learn from it.
Good luck.
