Question: how to evolve eevee into espeon in black 2?
Answer: To evolve an Eevee into Umbreon or Espeon quickly, you need to put a Sooth bell on it, when give it the berries that increase friendliness while decreaseing stats. ... 
I don't have this game but I do remember this from the Generation II games. ... 
Constantly use Eevee to make it happy towards you.