I play on the Xbox 360 as a Hunter and while doing the Shine A Light bounty for Eris Morn I noticed that Arcbolt Grenade kills didn't count toward the progress. I only needed three Arc or Solar kills to Complete the bounty and watched my grenade kill three enemies two or three times after thinking this might be a problem. I tested the other two Bladedancer grenades then, too, just to test and see if they worked or not, and they did. This was all in the same session as well. I didn't return to Orbit or move to a different zone on the planet I was on either. I also tested the other grenades on the same group of enemies, waiting for them to respawn each time before testing another grenade.
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Yeah, there was another post on here recently about arcbolt not being counted by that bounty. Not sure why, but all you can do for the time being is use a different grenade.