Is there an explosive method to destroying enemy helicopters while on foot?
My personal technique: I use assault rifle mounted grenade launcher. You do not have access to it directly at the beginning of the game, but still within the first area.
Just wait for the helicopter to be just above you, then fire your grenade launcher until the helicopter is down.
My solution to this is the HT1, sniper rifle.
It is a anti material rifle, and one shot is enought for any and all helicopter (2 with silencer).
Without bullet, you can try the drone (Explosive or IEM) or grenade launcher.