_(1) have somebody in your sights: to intend to attack or defeat someone.
- He's trying to build up his media empire and he has the owners of rival newspapers in his sights.
- After months of training, Hilary now has the gold medal firmly in her sights.
■ have someone or something in one's sights
_(1) Lit. to have one's gun aimed at someone or something.
- The sniper had the soldier in his sights.
- I had the deer in my sights. I fired.
- I have a promotion in my sights and I hope to get it before the end of the year.
- I've had Sally in my sights for years. I intend to marry her.
.... Cambridge Idioms Dictionary,
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs
■ sights as your aim/expectation
- Rossi has the defending champion in her sights in tomorrow's race. [have sb/sth in/within]
- After failing to get into university, he lowered his sights and got a job in a shop. [lower, raise]
- She has her sights set on becoming a writer. [set your sights on sth; have your sights set on sth]
- He says he wants to win the trophy, but I think he's setting his sights too high. [set your sights high/low]
.... Oxford Collocations Dictionary for Students of English