Spawn as Demolitions, instantly change to Berserker.
Alternative: If you don't have a level 6 Demo, your second choice is Medic or Firebug (free kevlar!). The M79 might prove useful during the next sections for clearing out swarms of trash but it is by no means a necessity. Same applies for the pipe bombs.

Only trash Zeds will spawn in this section of the map. Kite them!
Use the M79 to clear out multiple Crawlers from a safe distance before they can jump you.
Money should not be an issue, more to that later.

Buy an axe. That's all. Do NOT sell the pipe bombs. ONLY sell the M79 if you know exactly what you're doing. Otherwise refill its ammo to 12 rounds.

This is one of the more tedious parts of this map. You will have to kite while unwelding containers and looking for the two parts of the crane controls.
(Pro tip: Drop the M79 in front of the trader so you can pick up more weapons to sell. You will most likely not get much chance to use it here.)
Unweld all containers first before opening any of them. Kill only the bare minimum of Zeds.
(Rule of thumb: Kill only stuff that you can't out-maneuver.)
Only trash spawns out in the open, but red containers will spawn Sirens and Bloats when you open the wrong ones.
After you unwelded all containers, start opening them until you find the first part of the controls.
Pick it up, then open the rest. Do not pick up the second part the instant you find it; instead open the rest of the containers and kill what's inside.
If there's nothing inside, kill some trash Zeds and stuff will spawn inside. If you don't you might be in for a nasty surprise a few moments later.
Afterwards, grind trash Zeds until you are at about 1500 dosh.
Note: If your Support Specialist perk is not at level 6, grind some more until you can cover the cost for an AA-12+ammo and have at least 200 to spare.
The more you grind here, the sooner you are done with the REALLY tedious part later on.

Switch to Support Specialist. Sell your axe, buy an AA-12, kevlar and a backup shotgun.
Again, keep the pipes, you WILL need them later on. (Trust me on this.)
If you find yourself lacking in funds for even the basic shotgun, now is the moment you will have to part with the M79 (As I said, it is convenient, but not necessary).
Personal Recommendation: Get the HSG-1 or the normal shotgun for backup. The combat shotgun might look tempting due to its higher rate of fire, but that advantage is evened out by having to reload more often.

Pretty self-explanatory, really. Stand on the pressure plate, kill everything that moves.
(Or so one would think.)
One big disadvantage of this objective is that you have to stand on the pressure plate to complete it, so you will have to hold them off right there.
The brunt of the assault will come from the left and middle. After Halliday's announcement that they found another way in, there will also be attacks from the right.
Use your backup shotgun for single Zeds or smaller crowds.
If you kept the M79, use it to thin out crowds of weak Zeds at a distance, especially when there are Crawlers.
Only use the AA-12 for Scrakes and Fleshpounds or when you're getting swarmed and notice you can't hold them at bay otherwise.

Sell your backup shotgun.
Buy the combat shotgun and kevlar.
(You can now take your time to reload. Most of the time.)
Prioritise the AA-12 when restocking your ammo. You will possibly have to fend off multiple Fleshpounds.

Stand in this position, with the Trader to your left:
The Bloat's AI is programmed to make them jump into the machine when it is closer than you.
Other Zeds do not have that programming, so they should go for you instead, if they even get that close.
Avoid moving too much, use the M79 to take out swarms of weak Zeds at a distance and the combat shotgun for up close. Mind your shotguns' penetration, try to angle your shots so they do not hit the Bloats.
Again, only use the AA-12 against Scrakes or Fleshpounds or when you are getting swarmed.

You know the drill. You got your loadout, now grab whatever ammunition you can.

This is why I told you earlier to grind up some cash. Also, why I did not call "Export: Slaughter" the most tedious.
Pro tip: Set up a custom keybind to toss fewer dosh. It won't take ones, though
You have to win two cans of fuel by tossing dosh at the slot machines in the middle of the area.
They can, however, also spawn ammo or more Zeds.
There literally is no easy and fast way to do this. You will have to kite around the slot machines and throw dosh at them whenever they stop until two cans of gas drop.
Yet again, I cannot emphasise this often enough, only use the AA-12 for Scrakes, Fleshpounds and when you're under pressure.
However, this time it is a less pressing issue since the slot machines can drop ammo.

Do I really have to spell it out?

Here, you will have to hold out for two minutes.
The easiest way to do this is to just kite while keeping the killing to a minimum.
(Author's note: This is due to the fact that there can only be a maximum of 32 living Zeds on the map at a time.)
Again, only kill what you can't out-maneuver. Oh, and Fleshpounds. Always kill any Fleshpounds you see.

This is no real objective. You grab explosives, place them in the boat and refuel it.
You could, however, also use this time to pick a nice spot for the boss fight and place your pipe bombs if you still have them (which you totally should, by the way).
Personal Recommendation: Place pipes in this spot, stand behind the corner:

1. Buy kevlar.
   
2. Restock your AA-12 ammunition.
   
3. Buy pipe bombs.
   
4. All other ammunition
   
5. Place pipe bombs
   
6. If you still have dosh and time left, buy more pipe bombs.

If you read any other solo guides, you should know the drill.
Wait behind the corner (see above) and hit him with the AA-12 when he hits the pipes.
Chances are he will get away once; if he does, he will most likely heal right there in the yard with the slot machines. Reload, go after him, dump the entire mag into him. If that did not kill him, change to your combat shotgun and do it again.

Pretty self-explanatory. Go down to the pier and start the boat to send Halliday to hell.

FrightYard Objective Mode was one of the last maps I was missing. Having noticed that there were little objective mode guides at all, much less for FrightYard, I tried applying some of the strategies I learned in swenor's Steamland Objective Mode Guide, modifying them to suit the FrightYard objectives and my own play style.
That said, I do not claim to know the best or optimal way to beat FrightYard, so if you have constructive criticism to offer, feel free to do so.