There are 12 different kinds of achievements, each with 6 tiers.

• Open treasures
  
• Obtain gold
  
• Flip tiles
  
• Obtain equipment
  
• Obtain items
  
• Kill enemies
  
• Die
  
• Trigger mines
  
• Obtain runes
  
• Use items
  
• Refresh the shop
  
• Clear chapters

The required amount goes up for each tier (except for the chapter clear), for example Refresh Master (refresh the shop):

• I needs 50
  
• II needs 100
  
• III needs 200
  
• IV needs 500
  
• V needs 1000
  
• VI needs 2000

These are total, so after you unlocked the first tier, you need another 50 (not 100).
For the chapter clear achievements you only need to do the next chapter, meaning that each completed chapter will grant you an achievement.

Each achievement grants runes. The higher the tier, the more runes with the VI achievements granting 500. These runes have to be manually claimed by going to the achievement menu from the main menu of the game.

This achievement requires you to use 200, 400, 600, 1000, 2000 and 5000 items for the tiers.
This is bugged and also counts unsuccessfully attempting to use an item. So for this you can buy an item from the shop that reveals tiles, clear a level and then (before advancing to the next one), right click the item. Or buy a healing item and attempt to use it at full health.
Do this up to 5000 times and enjoy some runes.

You need 20, 50, 100, 200, 500 and 1000 deaths for this. Just start a run, click on mines until you die and repeat.
This will also give you some progress on the trigger mines achievement.

If you play as Apprentice Knight (default class) or Elf Hunter, you will also obtain a piece of equipment at the start of each run which gives you progress towards that achievement.

These are more difficult to farm than the previous ones, but can be done with the right setup:

• Kill enemies
  
• Trigger mines
  
• Refresh the shop
  
• Obtain items

You need to get the right skills/stats to become unkillable. Some examples to achieve that:

• High dodge chance + heal on dodge skill
  
• High defense and/or dodge + life on kill skill or lifesteal skill or crit lifesteal skill
  
• High HP + life on kill skill
  
• Very high lifesteal (through high damage or multiple stacks of the lifesteal skills)

Essentially you need enough damage reduction and life recovery to just tank every enemy. This becomes easier to achieve as you unlock more permanent upgrades and get further into the game (because early levels are so small that you barely gain any gold/experience, making it difficult to assemble an unkillable build).

This allows you to kill all enemies for the rest of the run to quickly get closer to the 1000 kills.
If you get the skill that grants you gold per kill, you can also buy a bunch of items from the shop and/or refresh it repeatedly. Preferably with the reduced shop/reroll cost skill.

For farming gold or runes you want gold/runes on kill, experience on kill (to get more skill points, though note that you can only go up to level 51!), more gold/rune gain and if you have a decent amount already then go for the gamble(s) to hopefully double it.
Runes/gold per level, per chest or per tiles cleared grant laughable amounts compared to on kill (if you can kill everything).
Getting over 20k gold or over 10k runes on one of these unkillable farming runs is not a rarity for me. With the right skills early on and some lucky gambles you could probably get over 50k. Note that this strategy is much more rewarding with later chapters because they have bigger levels with more enemies.

With this method you can farm most of the achievements, but those listed at the top of this section were the easiest to get some progress with.