Two months is too short a time to get into Google first page for "highly" competitive keywords.You may need atleast a period of 4 to 6 months for the results to show consistently.There is no fixed formula for SEO,you should be monitoring various sources of traffic and fine tuning link building and link placement.In general SEO consists of forum comments,blog comments (both from relevant topic sites),topical link building,press releases,article marketing,social networking,social book marking,etc.I hope this would help you get started.

My first concern would be for that of who you are working the project for. I am hoping that you did not guarantee them that you would get them there that fast. There is no set formula for getting your site ranked. There are things that you can do on a regular basis that will help you out. But what happens if those around start doing them as well? What are you going to do at that point? If the keywords that you are working for are that competitive then you are going to have to gain some respect in the search engine to beat those out that are above you. I don't see 2 months being near enough time for that to happen, especially if you are dealing with a new site.

Build high quality, dofollow backlinks using your keywords as anchor text.

depend on several things .

what are your current rankings ?
how old your site is ?
how many quality links it has ?
What is the level of competition for these keywords ?

bla bla bla

but if these are some really high competitive keywords then its not a simple task and you indeed need some serious link building and SEO skills .

Not sure about this post but probably the only way to get to the top for competitive terms in 2 months is by being very naughty and using the "black hat" techniques. You could acheive it but you might not stay there for long.

Better to check first the level of competition of that keywords before you start anything. If the competition is high, 2 months will not be enough.