Stage 1:
0:00 - Use mounted guns to kill enemies 14-20/20
Stage 2:
2:05 - Kill bleeding hostiles 18-20/20
3:01 - Neutralize Lt. Kelly in Air & Space Museum
Stage 3:
3:32 - Neutralize Wade in ViewPoint Museum, by breaking his helmet first
3:52 - Kill burning hostiles 15/15
4:10 - Take hostile convoy 03/03
Stage 4:
5:04 - Neutralize heavy weapons enemies in the open world 04-05/05 and Complete territory control activities 03/03
6:14 - Kill hostiles highlighted by Pulse 18-20/20
6:26 - Neutralize Ridgeway in the Capitol Stronghold, without using an armor kit
Stage 5:
7:03 - Neutralize Basilisk on Roosevelt Island, by destroying his armor first
7:14 - Kill hostiles with mounted weapons on Roosevelt Island 20/20
7:39 - Kill hostiles with an LMG in the open world 27-30/30
8:29 - Complete open world Activities 07/07
References:
"Stinger hive will do it" / kill_20_bleeding_hostiles
"Explosive damage are spread across the whole armour of an heavy. So it will strip him of all his armour before going for his health and killing him." / gunner_stage_5_field_r...