Fierce is an adjective that shows or describes a very high degree
A fierce competitor is a very determined competitor meaning they will keep trying to defeat their opponent even if it becomes very difficult
Ferocious and fierce are shown as synonyms in the dictionary, but ferocious has more of the violent meaning
The lion is ferocious and afraid of nothing
Fierce does not necessarily mean good or bad, usually surrounding context is used
He is fiercely competitive at chess (determined, can't really be violent at chess)
His fierce attack was successful (violent, sudden, and determined)
The dragon is a fierce beast (violent and scary)
The snow storm was fierce and claimed several lives (violent and strong)
Other examples as fiercely
Professional athletes are fiercely competitive and want to win
Mothers are fiercely protective of their young
Lions are fiercely aggressive to intruders
Soldiers are fiercely loyal to their leaders
these all describe a very high degree of what is being modified
Some more examples of fiercely can be found here