This is a Shotgun Boss Hunting Build that sacrifices a bit of its potential Shotgun power to also be decent at Melee (very economic $$).
I've seen many Shotgun + Melee builds and tried then but they all give no love to the Melee aspect of it, some with melee that does no damage, some with no tankiness (good for melee), some with both problems.
But what does being decent at melee mean?
Looking at the game bestiary (infected HPs) we can get the following information:
12 Damage: minimum for a melee weapon be relevant (1 to 3 hits=kill, except radiant fat male wich needs 4).
15.6 Damage: much better, at this damage we start to one hit both radiant childs and 2 hits radiant male (used to need 3 hits).
18 Damage: 1 to 2 hits every infected except radiant fat male (3 hits).
22.5 Damage: 1 to 2 hits every infected, a Melee build goal.
The goal here is to get 15.6 Damage at Level 30 (consistent) and 18 Damage at prestige 5 (a bit hard).
At level 30 with 25% Body Damage and 45% Infected Damage from gear, a Sledge Hammer and the stats from the Skills we accomplish that.
25% from Melee Expert V
25% from Gear
15% from Exterminator III
45% from Gear
15.96 > 15.6
Tips for Gear:
Commander's Helmet is great (with +25% Body Damage and +25% Damage vs Infected).
Recommend getting the remaining +20% Damage vs Infected on the Sledge Hammer.
The rest of the gear should be all about making Shotgun strong and be Tanky.
Body: look for - Incoming Damage and + Health. + Inventory Capacity if possible.
Legs: look for - Incoming Damage, + Health and + Jog Speed. More than +10% Inventory Capacity if possible.
Feet: look for + Jog Speed. More than -1% Incoming Damage and/or + Inventory Capacity if possible.
Weapons and Hands: look for + HS damage, + Damage vs Mutated, + Knockback Distance, + Stun Duration, - Incoming Damage, + Health, + Jog Speed (must have).
Try to get at least 65% Jog Speed to out run Tendrils in rooms.
Try to get at least -25% Incoming Damage and +130% Health (total) to be relevant at tanking.
Example of Gear
18 damage with melee at level 30 (17.98 seems to be equivalent to 18)
Ideally going to able to use Carlsen's Cap instead of Commander's Helmet at level 35 compensating the loss of Body Damage and Damage to Infected with better gear and +II Exterminator. Carlsen's Cap is great for boss hunting with Shotguns.