I'm not precisely sure what you mean by one verb "acting" on another because that could potentially means many things. Also, it seems your examples just deal with liking/hating something, so I'll answer according to that. In that case, the third one is correct. You first have to nominalize the verb by adding
こと to the dictionary form (辞書形).
- 踊るのが大好きです！ → I love to dance
- 戦うのが嫌い！ → I hate to fight
- 映画を見ることが趣味【しゅみ】です → Watching movies is a/my hobby
However, one verb can "act" on another with simply the
〜て form (and possibly various, "set" endings).
- チキンを焼いて食べる → I grill the chicken then eat it / I eat chicken by grilling it
- やってみる → Do something and see how it turns out -
それ、やってみよう！ → "Let's do it" (with some uncertainty)
- 本やペンを机の引き出しにしまっておく → Put away my books, pens, etc. in the desk drawer (so they'll be ready for next time)
Or different types of compound verbs
- 着替える → Change your clothes ("redo your dressing")
- 雨が降り出す → Begin raining
- 仕始める → Start doing
So I think "a verb acting upon another verb" could really cover a lot of different situations.
See also What is the difference between the nominalizers こと and の?