Exploration is an event which opens on every Sunday between 8:00 and 22:00 ingame time. You can catch corresponding epic monsters within given time. Also your power will be tested by spiritual monster Mew and if you pass, you will be able to collect one of those bugle parts.
You will also face eleven monster trainers, with greatly increasing power. You will be rewarded with tm shards and balls according to collected amount of stars.