During my first battle of my first play of Long War I threw a granade to a Sectoid. After exploding, it granted me automatically these three achievements:
Bada Boom (Kill 50 aliens with Explosive Weapons)
Welcoming Commitee (Kill 150 Aliens)
Pale Horse (Kill 500 aliens)
I have only played XCOM before with a cracked non-Steam version of the game.
For Long War I uninstalled the old XCOM and installed fresh a legitimate Steam version of the Game... It's odd that I got those achevements...