The fastest way will depend on what time and what location you are leaving.

For example, if you are leaving from Hakone Yumoto station at 9:18am on a weekday, the fastest way seems to be this route:

9:18 - 9:32
Hakone Yumoto to Odawara via Odakyu Tokyu Hakone #4

9:42 - 10:09
Odawara to Shinagawa via Kodama #632 Shinkansen

10:23 - 11:27
Shinagawa to Narita Airport via Narita Express #19

At other times, it will be faster to go to Tokyo and catch the Narita Express; still other time, fastest going to Nippori and connecting from Keisei Skyliner.

But generally, between 130 and 160 minutes from Hakone Yumoto to Narita Airport stations.