Ok after reading this thread I don't feel the answers given here are up to the mark.
Firstly there are not a lot do follow comment blogs. If you find them it's like finding an rare Pokemon.
So let's not go for just commenting.
Nextly I would recommend you go to the same niche or topic website read some posts and if you can put an guest post. Contact the webmaster and put in your guest post req. Surely you will get an response it would either yes or no. You can contact as many as you want.
This has made me get more backlinks than ever - create some awesome inforgraphics (infographics are usually images ..You can mostly find them on Pinterest). Email the same niche bloggers about the infographics. If they want to use your infographics tell them to give an source back to you.
You can easily send one infographics to hundreds of blogs.
So tell how this works for you.
Or else you can find dead links and send them your link to replace.
Here is the last thing - I've wrote the answer as it works much simpler way. Yes it does but it depends on how you take it into process. Your email should be well built. Don't go like - "Hey this link is dead replace this with mine." It will not work.
Be great while approaching.
If you need an good email template then PM me.