The Shock Trooper is all about survivability. You get increased health and damage protection plus a reduced Immunity cooldown. Even Adrenaline Burst can help with survivability indirectly if you use it to reset your Immunity cooldown. To take advantage of that survivability we want to use a short range weapon. The best short range weapon happens to be the Shotgun, though other weapons will work with this build too.
Specialization: Shock Trooper
8 Pistols (unlocks Shotguns)
12 Shotguns (unlocks Carnage)
12 Combat Armor (unlocks Shield Boost)
12 Assault Training (unlocks Adrenaline Burst & Fitness)
12 Fitness (unlocks Immunity)
12 Soldier / Shock Trooper
12 Spectre Training (unlocks Unity)
12 Charm or Intimidate
12 Barrier (Bonus Talent)
Combat Armor, Fitness, Soldier / Shock Trooper, Spectre Training, and Barrier all provide bonuses to survivability, mostly in the form of increased health. Some of them also increase damage. Combine that with the Shotgun and you have a powerful up close fighter.
The basic idea is to stay in close range at all times but still stay alive. User Barrier to boost your shields. If it wears off or the enemies push through it with damage, use Shield Boost to combat the damage for a short time. Finally, use Immunity when you can’t keep your shields up any longer.
In between those skills you should activate Carnage, so you can hopefully kill everything before the protection skills wear off. If all those skills go on cooldown, you can finally use Adrenaline Burst to reset all of them. In all this gives you about 80 seconds of protection, more than enough to kill anything except bosses.
If all your skills are on cooldown while fighting a boss, then you need your squad members to use biotics or techs to keep the boss disabled. Otherwise, run for cover and wait for your cooldowns to finish.
More Pistol ranks instead of Barrier ranks – You can sacrifice a few talent points in Barrier to get a higher Pistol rank. Your character won’t fit the theme as much, but you will gain the ability to snipe medium distance enemies occasionally. Your skills will still favor up close “shotgunning” though.
Rifles instead of Shotguns and Pistols – Assault Rifles are pretty good all around, but especially in short range just like Shotguns. Later rifles with good upgrades can do well at medium range, but they are best in close range when all of the bullets will hit. Without Shotguns, you can also move the 4 Pistol points into Sniper Rifles.
Lift or Singularity instead of Barrier – If you think you have good enough survivability, you can choose one of these immobilizing bonus talents instead to keep enemies in close range. Lift is one of the only abilities that affects bosses. Singularity is best against mobs of weaker enemies.