SEO for High competitive Keyword

Those competition metrics 40-54 are doable (medium competition I would say) but you will need some power so the most effective thing to do is buying expired domains / setting them up on seperate hostings / post content and link to the site you want to rank.

Can get a bit expensive of course so you can also consider renting links instead, you'll probably end up spending $300-$400/month on rented links to reach good positions and if you buy domains at auctions like GoDaddy (over priced) you'll probably spend around $5k-10k + a few thousand more for hosting but then you have a network that you can rank quite a few more sites with.

A cheaper way would be to buy up domains that have been dropped, those cost only the registration fee but they are a lot weaker (if they were strong they would've been bid on at the auctions or back ordered) so I have no idea how many you would need of them.

There's antoher way and that works based on finding domains that have been dropped ages ago but that pool is getting thinner every day so not sure how much success you will have with that. To read more about that method just Google "Hayden Domain Method" or something like that, he wrote a guide on the subject.

high quality links, updates and time

One month is a short time but you can definitely improve it. Do what nik0 suggested, pbns work quite well.

Also do some link-building of your own on forums/blogs/social bookmarking sites and various other places, they aren't as effective but should help. Just don't order spammy backlinks as that will hurt more than help.