I'll do them in order of following the Left Column, and then the Right Column downward as listed on the K.G.B. + Achievements Screen
Difficulty and Time done on a 10 points scale. (not an average)
Note: The ratings and tips are assuming you're playing in a way to try to help your team as best you can through many different methods.
Iron Kurtain - Take 1000 points of damage in a single life.
Difficulty: 3 Time: 5.5 Tip: Just play as Heavy and eventually this'll come up if you're at all good at knowing when to retreat.
Party Loyalty - Kill 50 Enemies within 3 seconds of them attacking your Medic
Diffuculty: 2 Time: 6.5 Tip: Protect your Medic and this'll slowly build up.
Division of Labor - Kill 20 Enemies with a Medic assisting you, where neither of you Die.
Difficulty: 9 Time: 8.5 Tip: Get some good skills as Heavy, and find a Medic with skills of his own.
Red Octoberfest - Earn a Domination for a Medic who's healing you.
Difficulty: 1.5 Time: 3.5 Tip: This'll just happen naturally. Just get kills while being healed.
Show Trial - Kill an Enemy with a Taunt.
Difficulty: 5.5 Time: 4.5 Tip: Humiliation is a chance to get this. Otherwise just get behind somebody immobile and unaware of you...as a Heavy, this might take some time.
Crime and Punishment - Kill 10 Enemies carrying your Intelligence
Difficulty: 2.5 Time: 5 Tip: Just play any fast paced CTF map (no Valve ones so far) and this'll come easy.
Class Struggle - Work with a Friendly Medic to kill a Heavy-Medic pair.
Difficulty: 1.5 Time: 2 Tip: Even playing heavy badly, this is a cinch that'll be a piece of cake during the Heavy rush; and a simple matter thereafter.
Soviet Block - While invulnerable and on defense, block an invulnerable enemy Heavy's movement.
Difficulty: 2 Time: 4 Tip: Play Dustbowl on Red, and this'll be a simple matter.
Stalin the Cart - Block the enemy from moving the payload cart 25 times.
Difficulty: 1.5 Time: 5 Tip: Just get next to the Cart while it's being pushed. Very easy to do early on in each section of either VALVe Payload map; as they both have a number of good places to jump down from.
Supreme Soviet - Get Ubered 50 times.
Difficulty: 2.5 Time: 9.5 Tip: If you look good then this'll move a bit quicker. This is just something you'll pick up from playing alot of Heavy.
Factory Worker - Kill 20 Enemies while being recharged by a dispenser.
Difficulty: 1.5 Time: 3.5 Tip: Get an engineer to set up a dispenser somewhere nice...and shoot...while standing next to the dispenser...with enemies in your crosshair...
Soviet Union - Get 25 enemy kills when you either assist, or are assisted by another Heavy.
Difficulty: 2 Time: 6.5 Tip: Just partner up with another Heavy and go...
Own the Means of Production - Get rid of 20 Sticky Bombs by killing the Demomen who produced them.
Difficulty: 3.5 Time: 4.5 Tip: Just don't get blown up.
Krazy Ivan - Kill 100 Enemies while both you and your Victim are Underwater
Difficulty: 3.5 Time: 10 Tip: Unless your playing the Troll under the Bridge in 2Fort, this one's going to take a LONG time...
Rasputin - In a single life, get shot, burned, bludgeoned, and receive explosive damage.
Difficulty: 3 Time: 6 Tip: Pretty similar to Iron Kurtain; though it'll probably take a bit longer.
Icing on the Cake - Get 20 kills on players that you're Dominating
Difficulty: 7.5 Time: 7 Tip: Get good enough to commonly Dominate as Heavy; then just pick it up as you go.
Crock Block - Survive a Direct Hit from a Critical Rocket
Difficulty: 1 Time: 6.5 Tip: Nothing much you can do but try to have high health alot.
Kollectivization - Get 1000 Assists
Difficulty: 2 Time: 8.5 Tip: I'm not sure if you can build this from getting kills where you're assisted...anyways, it's going to be quite the grind.
Spyalectical Materialism - Kill or assist in killing 10 cloaked spies.
Difficulty: 3.5 Time: 4.5 Tip: Look around a bit every now and then.
Permanent Revolution - Kill 5 enemies without spinning down your gun.
Difficulty: 4 Time: 6 Tip: Perfect to do along with Factory Worker...just sit next to a dispenser and play sentry.
Heavy Industry - Fire $200,000 worth of minigun rounds in a single life.
Note: Just watch "Meet the Heavy"...I say nothing more here...
Communist Mani-Fisto - Kill an enemy with a critical punch.
Difficulty: 3.5 Time: 4 Tip: ummm...Punch? (Actually, this should be pretty easy on the vertically focused "Badwater Basin"; just jump down from above and knock the snot outta them.)
Redistribution of Health - Heal 1000 damage with med-kits in a single life.
Difficulty: 5.5 Time: 6 Tip: Pretty much the same thing as "Iron Kurtain" only harder.
Rationing - Kill an enemy with your shotgun while you're out of minigun ammo.
Difficulty: 2.5 Time: 4 Tip: Not a problem as long as you've got some health...and a lack of minigun ammo.
Vanguard Party - Be the first on your team to start capturing a control point in a round.
Difficulty: 1.5 Time: 7 Tip: Just have to wait until it happens pretty much; shouldn't be too hard on granary.
Pushkin the Kart - Get 50 caps on payload maps.
Difficulty: 2.5 Time: 7 Tip: Just play Payload maps enough for it to happen; and make sure to stay near the cart while pushing through.
Marxman - Kill 10 enemies in mid-air with the minigun.
Difficulty: 3.5 Time: 7.5 Tip: Keep an eye on any enemy Soldiers; lest they Rocket Jump without you getting a chance to fire at them. Natascha should be good for this.
Gorky Parked - Kill 25 enemies while you're standing on a control point you own.
Difficulty: 2.5 Time: 6.5 Tip: Set yourself up on a friendly point (hopefully with a dispenser), and do some simple defense.
Purge - Kill 15 enemies capturing a control point you own.
Difficulty: 3 Time: 5.5 Tip: Just be ready to protect any nearby points of your team's that could be attacked anytime soon.
Lenin A Hand - Help 5 teammates get revenge on their nemeses.
Difficulty: 1.5 Time: 7 Tip: Basically just plain luck...with a bit of a boost if you've got a Medic. (incase they're dominated that is)
Five Second Plan - Kill an enemy in the first 5 seconds after you exit a teleporter.
Note: Not sure if you can go through a tele and stay revved or not...
Difficulty: 3.5 Time: 6.5 Tip: Be ready to attack after you teleport...nothing much to it but that.
Photostroika - Provide an enemy with a freezecam shot of you taunting while invulnerable.
Note: Do this after wiping out an entire group, or in humiliation...otherwise your a griefer.
Difficulty: 2 Time: 7.5 Tip: Know what the taunt key is and be ready to use it when you need to.
Konspicuous Konsumption - Eat 100 sandviches.
Difficulty: ? Time: ? Tip: Yum.
Don't Touch Sandvich - Kill 50 scouts using Natascha.
Difficulty: 2.5 Time: 6.5 Tip: Just play with "Natascha", and you'll pick this one up in time.
Borscht Belt - Kill 10 heavies with The K.G.B.
Difficulty: 4.5 Time: 6.5 Tip: This could actually be a realistic thing to do while ubered...have to wait and see just how good the KGBs are.
Note: Finished writing this before; guess it didn't process right when I posted the edit.