Its_A_Random, you accepted the other Pachi and not mine? You must catch the first Burmy you find. The restrictions depend on the gender.
If it's a male, he must be named "Moth" and must keep Hidden Power upon learning it. As a Mothim he must solo 20 Pokemon that resist his Hidden Power (no immunity, please!), with Hidden Power alone.
If it's a female, she must be called "Cloak". As a Wormadam she must solo 20 Pokemon whose type matches her cloak's secondary type.