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 の
or 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?