From Halopedia, the Halo wiki
Eavesdropping is an achievement in Halo: The Master Chief Collection. It is awarded for activating the sixth Halo 3: ODST Audio log on Mombasa Streets. The achievement is worth 5 Gamerscore and can be unlocked on any difficulty.
The achievement is awarded when the player unlocks their sixth terminal, regardless of which terminal in the hub that is. For terminal locations, see here.