How google ranks your site is a combination of many factors, only Google engineers fully know what they are and how they are weighted. There are people that have invested a lot of time and effort in understanding this, to the extent they have domains set up specifically as control points and have analyzed data from them over decades. They use that data to manage changes to their main sites or the sites of their clients. Setting aside content some of the important things are markup, mobile ready, https, server speed and the list goes on and on. server speed, markup, https, mobile friendly etc.
To target specific keywords you can start by having a lot of unique content that covers them. Internally and externally links using anchor text that contains those words are important but they need to be linking to pages that are relevant to them. This naturally occurs internally, one improvement that could be made th this is automatically using topic title instead of the URL. It's easy to do yourself but most members are not going to go through the effort. External links from good sites that can improve your results come naturally with good content.
There is lots of improvements that can be made with phpBB, some minor things like using <h1> for unique titles on pages instead of the site name. Others not so minor like a sitemap. Quick tip, it's not quite as effective but if you have webmaster account for Google you can substitute the RSS feeds as sitemap.
“Results! Why, man, I have gotten a lot of results! I have found several thousand things that won’t work.”