It is important to note that there are several sequences in the film that will not count for kills. There are several dream sequences as well as an overlap at the beginning of the film where the deaths within are concurrent with what occurred in Man of Steel. All deaths between 5:58 and 7:51 fall into the latter category and will be added to that kill count when it is created.
5:58 Two drivers blown up.
7:51 Bruce’s friend Jack dies in building collapse (It is unclear if the other staff clear the building before it is levelled)
15:01 Jimmy shot by terrorist
15:51 Guy that shot jimmy shoots 3 terrorists
16:08 Another in his unit guns down 2 more and another gets 2 more
16:18 Two more terrorists down
17:54 Terrorist leader taken through multiple walls by supes
59:45 Inmate stabbed to death
1:12:00 It is at about this point that Bruce confirms that there were thousands killed in the battle during Man of Steel
1:16:29 Batman flips a car on 2 guys
1:16:52 Batman guns down a gunner and probably the driver of his car
1:17:40 Two guys run into a fuel tanker
1:18:01 Bats kills 1 guys in the back of a semi
1:28:03 Woman pushed in front of train
1:30:30 At least 118 die in explosion in capitol
2:15:58 Four gunners die by bat plane
2:17:13 Two thugs taken out by grenade
2:17:30 Bats kills a guy with a crate
2:19:21 Bats blows up a guy with his own flamethrower
2:23:33 Doomsday destroys an airborne helicopter so we can assume at least a pilot died
2:24:47 Doomsday takes out another, so again at least 1, he then explodes after taking fire from another aircraft and it is gone after that so chalk up another pilot
2:38:42 Supes and ‘doomsday’ die
Total: 153
Here is a kill count ranking by Gamespy that is interesting. It counts the overlaps with Man of Steel that I do not and estimates numbers with no real basis that I can see (though it is still plausible).