- He ran quickly down the hill.
- He dashed down the hill.
I tell anyone who'll listen that "adverbs are not your friends" and this is one reason for that. When I encounter a lame verb-adverb combo, I ask if my treasure store of vocabulary contains a fitting verb that can replace it.
I don't recommend the writer ever rely upon the Thesaurus, except as a reminder for words you already know. Every word carries nuance that the writer needs to fully understand or s/he risks foolishly saying something unintended.
This is particularly important when writing the action scene. Every word counts in an action scene. Here's something I'm working on now:
Makeda sprang forward as Nell leapt to her feet. She wheeled on the Nubian, drew her stunner and cut him down. He convulsed and fell in a heap with his sword clattering on the floor.
Note the verbs: sprang, leapt, wheeled, drew, cut, convulsed, and fell. Can you imagine how lame it would be to replace these verbs with adverbial phrases like "ran quickly?"