This achievement isn't really as hard as the following solution will make it seem, but it can be picky and a bit of a time waster so I thought it better to note down as much about it as possible than not. Don't worry; it's actually quite easy if you know what you're doing. This solution is about letting you know just that!
You are going to need one fully-maxed out ranged character; I used Garth. Next, you're going to need three preferrably ranged characters that aren't necessarily level 1, but as low as you can keep them. No damage buffs or anything.
With the above setup of a strong Garth and crappy other ranged characters, you can pretty much kill everything before the other characters get a shot off which yields both more kills and coins. Your focus should be on killing the mobs, then mopping up the gold before it disappears. Try to get kills before the AI does as doing damage and getting kills give you more gold than simply picking up coins does. The only time I'd prioritze money over killing is when the enemies dropped the huge coins.
When you max out a character, you get access to the Inner Board on the Abilities Board. These are the real key to getting gold medals. Which of the Inner Board perks are the best really depends on the level, but as long as you land on either the one the adds +1 to your multiplier or Coin Magnet, you can give pretty much any level a shot. Some levels are even doable without any perks, while others can be done with just damage-buffing ones. If you find that the perk you went with doesn't work out for the level you picked, you can quit out before finishing the level and keep the perk for another level. See below for more tips on that.
As for whether to use the boss or the minigame at the end of the level, it all boils down to how much money you have you when get to the intersection. The normal minigames give 5000 for a win, and the dark ones give 10000. So, obviously, if you have 2000 left to go for the gold, pick the minigame. Your multiplier doesn't matter there so as long as you win, which is very easy against the AI players, you're guaranteed the gold from that point. The boss route depends on the level; I never had much luck getting gold from the one in Hobbe Caves but the one in Aurora gives tons of gold both during the boss fight and on the path to it.
Great tip from Weezleram: every boss has a point where it will continuously spawn enemies as long as you don't kill him. If you have 4 players then you can keep the boss alive forever and just have him keep spawning enemies to kill and gain coins from. If you have three extra controllers you can have them jump in when you get to the boss (so you won't have to keep taking time to move them forward and losing your multiplier) by turning the controller on, pressing start, and logging in as a guest. Then you can just kill the spawned enemies and there will be no AI to finish off the boss.
Last note: why not a melee character? It's doable too, but using a ranged one is just much easier.
* If you have a good setup for a level, like having both the +1 multiplier and a couple of other good ones from Inner Board, but you don't quite reach the gold for whatever reason (main one being the AI being a dick and hogging all the gold), you can just pause and restart and it does not reset your Inner Board perks.
* Also, this still works if you quit the level. If you had perks that are good but weren't enough for that specific level, you don't have to finish it and go back to the board game in the hopes of getting good perks again. Just quit to the level select and you'll still have the perks in whatever level you choose to play next. Perks do not reset until you actually complete a level.
* You can play on Normal or Challenging difficulty, but not Family. In my experience, Challenging did give you a few extra coins but it's not enough to warrant the higher chance of getting hit. Stick with Normal.
Gold medal requirements!
I've included my personal rating of how hard it was to get the gold on each level, on a 5 star scale where 5 is hard and 1 is a joke. A 5 star rating doesn't mean that it's incredibly hard though; just that it's harder than the other levels. Basically, on some levels, you can rush and still get several thousand above gold while on others, you have to pick up every single coin dropped and still barely make it past the gold.
Millfields: 30,000 [**---]
Gravestone: 25,000 [*----]
Mistpeak: 40,000 [***--]
The Cloud: 65,000 [*****] (Use the right-most teleporter every time.)
Hobbe Caves: 45,000 [****-]
Bowerstone: 50,000 [*----]
Aurora: 60,000 [****-] (The boss route yields more than you might think.)
The Credits: 55,000 [*----] (Destroy the developer names.)
Millfields: 60,000 [***--]
Gravestone: 40,000 [*----]
Mistpeak: 70,000 [**---]
The Cloud: 90,000 [*****] (Use the right-most teleporter every time.)
Hobbe Caves: 65,000 [***--]
Bowerstone: 35,000 [*----]
Aurora: 90,000 [****-] (The boss route yields more than you might think.)
The Credits: 70,000 [*----] (Destroy the developer names.)
NOTE: Dark Albion medals!
The gold medals in Dark Albion are very hard to distinguish from silvers, due to the dark hue of the whole map. There is a slight difference, but you might even have to change the color/contrast settings on your TV to see it! The silver is a very clear, chrome-ish silver while the gold medal looks like a slightly dirty silver. The difference is miniscule, but it's there. I suggest that you keep notes of what Dark Albion levels you've gotten golds on, to avoid any potential future headaches.
CREDIT goes to xhunterr, IC3 L3G3ND, erico360, tripleb2k and many others here at TA and over at x360a. Finding out everything about this was a collaborative effort.