That megamenu is giving that page too many external links.

Choose a main keyword for each page and optimize for it, choose some (few sematically related) secondary keywords and try to optimize the page for them without jeopardaizing the first.

Please go again through MOZ guides and blog post and very nice whiteboard friday videos to better understand what "optimize" mean.

Once done if you will look back at the source code of those pages you will notice yourself they don't smell nicely.

Depending on the keyword competition level you may need to get some backlinks for those keywords, which means generate good quality links from relevant websites, within relevant content, without a spammy anchor, etc...

Work page by page, keyword by keyword. It's a long and draining process.

If I look at your backlink profile with ahrefs, there's few I don't like, I am referring to anchortexts stuffed with keywords which doesn't look natural to me, and I assume google would not consider them natural either.

Your competitor pinkcherry doesn't look much better, but that should not give you much comfort. And btw they have much more linking root domains so they beat you anyhow.

It's the on page which is really an issue in my opinion. Just starting with following advices from MOZ page grader would help a lot.

Take this page http://www.cupidboutique.com/vibrators which I assume from your early comment you would like to see ranked better than your competitors for the keyword "vibrators", and look at the source code. Starting from the head there's a lot I don't like, if you want to rank for vibrators, trim the title, that megamenu is overkilling with external links, the keyword density is overwhelming, and 50 h2 tag are simply too much. And content is thin.

You should rethink it. If you look at hushcanada.com page source for their best ranking results for the keyword vibrators you will see it's much much much better.

Pinkcherry rules because of the links, hushcanada beat you because of their onpage.

I can see the total number of referring domains decreasing for cupidboutique.com while it's increasing for the two others. That's not good.

Usual metrics, like DA/Trust etc... are definitely better for pinkcherry who also has more backlinks, but cupidboutique values are supposely better than hushcanada.

But... The count of positions in SERP top 50 is surprisingly low for cupidboutique (209) when compared to pinkcherry (1.2k) and hushcanada (823), something is definitely wrong with your SEO on-page in my opinion; but it could also be your backlink profile, you should check anchor text diversity and backlink diversity.

In addition to all the good answers you already got.

Putting everything on a single page you lose opportunities to place keywords in url, <title>and <h1> or diluting <h1> value.</p></title>

I would be surprised.

Google knows a lot, but not everything. Unless GA tracking code is installed google shall not know about things such a user click.

If they were passing page juices only for clicked backlink they would be ruling out a too big chunk of the web. It doesn't sound logic to me.

Also it doesn't sound realistic to analyze all users click in the world when refreshing google index, they do have a lot of metal, but not that much.

targeting the keywords with the highest volume can be misleading, they are not necessary the best converting keywords, and since usually everyone prefer to shot at the biggest target competition is fierce

I am not saying it's wrong, but I would be more selective and choose keywords on the base of a variety of factors.

I have seen google algo rank the same page for very similar phrases where the keywords where just changing places, but it's not "always" doing it. You can help him learn that page is a good fit for both queries with the copy of the page.

google knows about synonyms and does often show same or very similar SERP for different keywords which are considered to have the same "exact" meaning and usage in language. But in my experience does treat plurals in a different way.

I would use exact match for title and exact match for h1 if it make sense, but avoiding using unnatural language.

Unfortunatelly SEO is a land where certainity is scarce, and I would recommend testing different versions to find out what works best in your case.

In theory they should discount it.

Usually it takes time. I have a domain I bought to test this technique two years ago, it had DA56, now it's DA20, that's giving you an idea of how slowly they do.

But I have also seen domain being bought, content changed, and still retain their value.

No one knows what is in the mind of google algo.