Hand of Fate

Note - if you buy the DLC, you'll need all DLC cards if you haven't unlocked this prior.
This also means you'll need to do the Apprentice and Warlord cards even if you don't own the DLC, as you have them by default.
Note - Since first writing this guide there has been a new Title Update that has added more cards. If there is anything difficult about these cards that makes it so this guide does not suffice I will add to it.

To unlock more equipment or encounters, you want to use cards that have the little token symbols at the bottom. This means, if you play the encounter right, you unlock more cards. Some of the harder encounters require quite a bit of food/money/luck or some combination therein. As the wiki does a good job of explaining individual cards, I would recommend using that.

My main purpose for writing the guide is to state that it would likely be best to work on this (or at least your last few harder cards) on Apprentice difficulty. Playing on apprentice does not stop you from unlocking more cards, and as it is easier, you'll generally have more resources for the resource intensive cards.

Some cards have really weird outcomes to reward the token (one I can remember requires you to fail and then huge success.) Look for the outcomes that say 'Rewards a token.'
http://handoffate.gamepedia.com/Hand_of_Fate_Wiki

I'd recommend using for the Warlord cards, although even when the achievement unlocks there are still a couple more cards after it.

Most easier cards I just focused on during the 'story'. While the same Warlords guide suggested doing Jack of Skulls for certain encounters, I found myself more often than not ending up against two bosses just about every fight. Most cards other than the Warlord ones where you need to have certain equipment I'd recommend endless mode.

I tried doing Blacksmith (from Warlord 3) on Jack of Skulls but I just never had any decent supplies by the time I found it. The first time I found it in endless I beat it. I mean mainly it comes down to luck, I'm sure some people will do fine retrying Jack of Skulls for it. For some reason if you go back to older court cards it seems to keep the farther ones in the deck, so you can end up against harder bosses or even the boss you're supposed to be looking for. But on endless mode you only start with 2/3 of dust and then he adds cards from there.

Note - I couldn't get Huge Success to show up for Wheel of the Gods on Apprentice. Wheel of the Gods is a normal encounter AND a Warlord encounter when you unlock it, so you can play on Warlord for 2 chances at it.
Update - Lockie has stated you must play on Warlord for Huge Success to even appear.
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Step by Step
1. Focus on getting tokens during the 'story' - use the wiki for token outcomes, some aren't obvious.
2. Endless Apprentice for most of the rest. Or Jack of Skulls if you prefer restarting when you can't find what you need.
3. Warlord encounters, use the guide for that specific achievement.
4. Blacksmith - I recommend endless Warlord personally.
5. Post-Blacksmith - Endless Apprentice again. (Only a couple cards) Or you could do the Jack of Skulls retries since there aren't too many assuming you've unlocked everything else.