I don't totally understand the mechanism either, but I will say that the swarm levels are your best bet to amass the 300+ kill amulets. I got 900 consecutive kills in one of the swarm levels ^^
You don't have to kill them in one hit I don't think, because I've had kill counts proceed through Giant Monster waves, so there is some mechanism for determining when a kill string starts and stops, but I don't know what it is.
I think it's pretty tricky where the border for a chain continuation is, but as long as there is a kill every moment (short moments), the chain remains.
I think I did a 1253 chain in a swarm level. Pretty sweet.
I think the requirement is that of all your active towers, they should not all miss a firing cycle continuously. so as long as a tower is firing continuously, the "in a row" counter" updates. As soon as all your towers do not have a monster to fire at when they are ready, then the counter resets..... I think.
Secondly, are y'all talking about a different chapter of gemcraft, because I don't see any indicator of number of kills or an amulet requiring 300+ kills.
I'm playing through the chapter one first, so I'm guessing all yoru advice is for the wrong game and I hope somehow translates.
I think it's pretty much the same for chapter 1, though I recall that as being a bit easier. Just keep calling the waves early so your gems always have something to shoot at.