How do you get real targeted Twitter followers?

Follow targeted people on your niche. You can use tools like for example https://followerwonk.com/bio/?q=cooking&q_type=all&l=united states to search for targeted twitter profiles.

Post useful stuff and retweet posts that are sensible.

Try to become a celebrity. LOL

start following, re tweeting , re sharing heavily

I scrape and follow the followers of my competitors (with a bot and with fake accounts); then whith my main account I manually follow (no bot) who does follow4follow.
I add to favorite the tweet of my competitors so others can see my picture.
I often retweet my followers.
I generally use this method but you can see your niche.

There are certain creative and innovative services in the Marketplace Section which you can have a look at.

These provide real looking Twitter followers which retweet and favorite all your tweets eventually making you look more popular and helping you get a lot of attention from other users on Twitter which eventually end up following you and becoming your potential clients.