The light shogun is nice and all, but even with AP loaded, it can not 1-shot a Hydra.
They have 40 hp and 8 armor (if I remember correctly) while the light shotgun has 15 base damage + AP makes it up to 35 Damage, either leaving hydras (with armor penetration effect) at 5 hp or (without it) at 13 hp.
However if an AP light shotgun can 1-shot hydras, then the damage is of its description is a lie, since you also have to think about bullet spread. The same story would also go for creepers, webbers and other armored enemies.
The heavy shotgun would remove those problems, due to higher base damage. The increased supply cost for reloading and reduced attack speed is worth the effect - at least for me.
I remember back in 2015 when the Agent was op... Rest in supplies, my friend.