Baichung Bhutia is an iconic figure from Sikkim, known for his achievements in:

Baichung Bhutia is an iconic figure from Sikkim, known for his achievements in football (soccer). He is the former captain of the Indian national football team and is considered to be one of the greatest Indian footballers of all time. He is also the founder of the Indian Super League (ISL).

Archery is a popular sport in Sikkim, but Baichung Bhutia is not known for his achievements in this sport.

Cricket is also a popular sport in Sikkim, but Baichung Bhutia is not known for his achievements in this sport either.

Politics is not a field in which Baichung Bhutia has achieved any notable success.

Therefore, the correct answer to the question is: a) Football (soccer).