mate, forget the DA metric! Quality links doesn't mean high DA (although, I admit, sometimes the higher the DA / DR metrics are the more reflective of a website's authority they are, but that still doesn't mean that they're high quality links, per se)
High quality links mean links that...
- get clicked on
- are placed in-content (not in sidebar, not in footer, not in pages with 100s of other links and no content... although, homepage links are good if they're placed on the homepages of quality sites)
- come from sites NOT seen as link farms by google (link farms are sites that exist only to sell links, so if you buy links from sites that have OBLs on every single content page then that link could be considered useless, or could become useless when google figures out that it comes from a link farm)
- come from sites that get decent organic traffic (I usually like to see at least a few 100s visitors a month, but other people will not consider links from sites that don't get a few 1000s visitors a month, so it's up to you what you consider "decent traffic", but the point is that you want the site that gives you the link to be indexed and ranking in google, otherwise it's worthless)
.. there are probably more things you need to check to make sure that you're getting quality links, but I don't remember them at the moment...
And like
@nahid133 said, web 2.0s are worthless, you can get 1000 of them and they'll barely do you any good. Few years ago web 2.0s used to work, but then google realized that everyone and their dog can get these links because they're free and easy to get, so they've devalued them. I built over 100 web 2.0s to one of my sites last year and they haven't even gotten my site in top 100 lol... It's true that the niche of my site had been competitive (pregnancy), but at least I should have seem some movement, an increase in impressions at least or something... Nope, nothing, nada! Not to mention that after 1-2 months most links have been deindexed by google, or my web 2.0s accounts banned, or the links have been tagged with the "nofollow" tag which makes them useless, and so on...
Anyway, just run a backlinks and content audit for both your site, and your competitor's site with a good audit software (Screaming Frog, Web CEO, etc... there's plenty of them out there) and see where the major differences between your site and your competitor's site are, and see what you can fix. If you can't fix anything, or there are no major differences it's probably the links (your competitor has more, or better links than you), or the topical relevancy of your competitor's site over yours... or maybe google trusts your competitor's site more because it's more aged... or maybe your competitor's content is more in-depth and or topically relevant to both the main keyword and the site's overall topical relevance... one of these things for sure (unless your site is sandboxed, as I mentioned previously, this could also be the problem)