Getting to the popular page currently requires:
-an aged account (over 3 months)
-the account has to be used regularly (upload images, follow other people, like their images)
-at least 20% of your followers to like the image (the one you want to get to 'popular')
-if you aren't an established user then the only links in your profile can be to your social media channels (though I've seen tumblr hit adversely recently)
-best not to tag the image with too many tags (the more 'popular' tags you use the more difficult it will be to get to the popular page)
-all the above within a 90 minute time frame (used to be shorter)
I think that's about it