The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
For generally effective villains, see Sliding Scale of Villain Effectiveness, under the Credible to Infinite sections. They come in many types and it's divided into how they are effective or how they demonstrate their effectiveness.
A villain succeeding at phase one of a multi-phase plan, like your example of taking over Earth as a stepping stone to a higher goal, is You Can't Thwart Stage One. It's quite common for villains to succeed at early stages of a plan and the heroes dramatically stop them when the stakes are much higher.
That sounds promising, thank you!
I know we have a lot of tropes for villains that are harmless and incompetent. But do we have tropes for villains which are the opposite (very competent)?
I require it for a Big Bad from a work for which I'm currently in the process of creating a page. The character in question single-handedly (as in: they alone without any help or Mooks) took over Earth while the heroes were offworld, a feat no other villain in that work had managed before (which include the previous Big Bad, a technologically and physically superior alien species which has been conquering and destroying planets for thousands of years and which also invaded when the heroes were offworld). And the character did it in just 10 hours. Taking over the Earth wasn't their goal, however, so it's not a case of The Bad Guy Wins. Rather, the villain just wanted to use Earth as leverage against the protagonist to surrender themself as the villain has a Villainous Crush on said protagonist.