So, there are a bunch of parameters listed out in other threads based on the forum software that blizz uses, not necessarily their specific parameters.
They can get to trust level 3 by…
This is time and activity based, unlike the previous levels. In the last 100 days…
must have visited at least 50% of days
must have replied to at least 10 different topics
of topics created in the last 100 days, must have viewed 25% (capped at 500)
of posts created in the last 100 days, must have read 25% (capped at 20k)
must have received 20 likes, and given 30 likes. These likes must be across a minimum number of different users (1/5 the number), across a minimum number of different days (1/4 the number). Likes cannot be from PMs.
must not have received more than 5 spam or offensive flags (with unique posts and unique users for each, confirmed by a moderator)
must not have been suspended