You can get this easily enough in the first mission after the tutorial.
The chain counter increments by one each time you kill an enemy. You have to kill enemies within a few seconds of each other else the counter resets. The time limit between each kill isn't strict so you shouldn't have too much trouble with this.
The counter will not reset if you get hit by enemy fire, but will reset if you get knocked down by an enemy and have to tap
to get up again.
The maximum possible chain on this map is 138 so if you get reset after 38 you will need to restart.
I did this on my first try with Cactus, but you may find Holly easier as her primary weapon seeks out enemies (you still have to be in range though).