The correct option is
C badly / worse / worst
The correct answer is Option B.
There is a comparison being made between 3 horses in the given sentence. Thus the degree of comparison of the adverb will be used. The first horse ran BADLY (this is the adverb which describes the manner of running).
The second horse ran WORSE and the last horse ran WORST.
BADLY- WORSE- WORST is the degree of comparison for the word BADLY.
The first horse will be described in the positive degree.
The second will be in the comparative degree.
The third will be in the superlative degree because comparison is being made more than 2 horses.
The remaining options are incorrect because:
Option A: It is not the degree of comparison.
Option C: It is an expression of degree of comparison but the first word is not an adverb that will describe the verb running.
Option D: It is not the degree of comparison.