Tiny Tina's Wonderlands

After completing the final story quest, the epilogue will walk you through accessing the Chaos Chamber and explain how it works by having you do a tutorial run of the Chamber (note that this tutorial run doesn't unlock Thank the Maker (50G) because it isn't a full run, which is what that achievement requires). Once you're done with the tutorial, you can begin doing full runs of the Chaos Chamber. There is a new of new stuff here, so in this achievement solution I will provide:
 

1. An explanation of how this mode works
2. What exactly you need to do to unlock these achievements
3. General tips and advice to make this as easy as possible

How this mode works
While the gameplay is the same as the encounters from the main game, there is one important change to note: you get 3 lives per run. So, dying doesn't end your run, it just puts you back at the start of your current encounter. You also don't lose any money when you lose a life. If you lose all lives, you obviously have to start the entire run over again.

Each run of the Chaos Chamber is structured the same way:
 

1. You will go through two or three standard combat encounters like you've seen in the main game. After the first combat encounter, the Dragon Lord will make you choose between two different negative modifiers (more on this below)
2. You will have a miniboss fight (typically where you kill enough enemies to shatter an obelisk in the center, releasing the miniboss for you to fight)
3. You will go through three or four more standard combat encounters (depending on how many you had before the miniboss) 
4. You will finish with a boss fight. You will fight against a random boss from the main game, in the same arena you fought it in the main game

After the first combat encounter, you will always be forced to choose a negative modifier from the Dragon Lord. You'll be able to see the names of each, and their difficulty level, but you won't be able to see what they do (but there are only a set amount, so you'll come to remember them all and what they do). For the purposes of these achievements, there is no reason to ever choose anything except the lowest difficulty option. Pay attention to what the main status change is on the left side and be prepared for it. It lasts through the entirety of the current run.

During all regular combat encounters, there will be a secondary objective. Just like in the main game, completing it only increases the rewards (crystals, loot, money) when you finish that encounter. From an achievement perspective, there is no need to worry about the secondary objectives.

After each combat encounter, you'll be presented with two portal options. Again, there is no description for what each is, but here is a quick rundown:
 

• Chest - there are two different treasure chest icons. The smaller brown one is for loot and the spikier one is for crystals. In both cases, after clearing the next encounter, there will be a giant Lucky Dice between the smaller ones, and breaking it either grants you far more crystals or some loot, depending on which chest portal you chose. In my opinion and experience, the loot was always bad, so I recommend always opting for the crystal chest over the loot chest
• Butt Stallion - after clearing the next encounter, Butt Stallion will be standing between the two small dice, and she will grant you additional skill points to a random skill in one of your trees (but only one you've already invested at least one point in). It was always either +2 or +3 skill points for me. This is incredibly good, so always choose this option when it's available
• Dragon Lord - after clearing the next encounter, Dragon Lord will be standing between the two small dice, and he will require you to choose another negative modifier, stacking with the one you already have. This is the worst option, so never ever choose it

So you should always, always choose the Butt Stallion portal if it's an option. Your second option should be the spikier chest for more crystals; third option is the loot chest, and you should never need to choose the Dragon Lord option for more negative modifiers.

Lastly are the crystals, which are a new currency specific to Chaos Chamber. They randomly drop from enemies in every encounter, and you can sometimes find hidden ones in encounters, but it's not worth it to waste time trying to hunt them down. These crystals can be spent on two things:
 

• During every encounter you'll see little shrines (marked as purple circles on your minimap) around the area, and you can pay crystals to buff a specific stat for the rest of this run. They get progressively more expensive the more you buy
• At the end of each run, after beating the boss and going through the gold portal, you'll come to a loot chamber. There are shrines lining both sides where you can spend crystals to get specific loot. If you're after something specific (like a really good pistol, or an orange class mod, or whatever), then I highly recommend saving up 500 crystals each run to spend where you want. If you use 500, you're guaranteed at least a couple purple of that item, and there's a good chance you'll get an orange too

How to unlock these achievements
While it may seem straightforward, it's actually a bit odd the way it's structured, so I want to quickly explain what exactly you need to do for these achievements.

When you talk to the Dragon Lord, you'll be able to scroll left and right to different types of Chaos Chamber runs, such as Featured Runs, Normal, Extended, etc. For these achievements, you must scroll over to Chaos Trial. The description says it will increase your Chaos level, so that's what you want. Complete your first Chaos Trial and it'll tell you that you unlocked Chaos Level 2. Now the finicky and important part. When you talk to Dragon Lord to start your next run, you will likely still be on the Chaos Trials tab. DO NOT just start another trial to increase your level again. First, you must scroll over to any of the other tabs, then go to the Chaos Level slider and increase your Chaos Level to the max (it'll be level 2 right now), then scroll back to Chaos Trials, and now you can start your next Chaos Trial, playing on the highest level you have so that you unlock the next level. Make sure to repeat this each time, otherwise your Chaos Trial runs are pointless if you forget to scroll over and increase your Chaos Level each time. Also worth noting is that, other than Chaos Trials, every other type of run is completely unnecessary from an achievement perspective. 

Once you actually unlock Chaos Level 20, you will unlock this achievement. No need to actually play through and complete a run on Chaos Level 20.

General tips and advice
Lastly is a collection of tips and advice based on my experience with this mode.
 

• If you weren't playing the main game on the easiest difficulty, I highly recommend going into the options and lowering the game difficulty to the easiest for this mode
• Reach level 40 and equip your best gear (obviously)
• With your best gear, you should have tons of Moon Orbs from completing everything in the main game. Head to the anvil near Dragon Lord and use it to enchant all the gear you're using. Reroll enchantments until you get ones that are perfect for your playstyle. For example. I built my character entirely around damage output and critical hits, so my shield granted +30% gun damage on Action Skill activiation, my melee weapon granted +28% gun damage on Action Skill activiation, my spell granted +11% all damage on spell use, etc. This made me an absolute beast when I'd use my Action Skill to demolish mobs and bosses. This will need to be catered to your weapons and playstyle though, but enchant everything you use, because there are no bad enchantments, just useless ones if you aren't capitalizing on them. Enchantments can be more valuable than the loot stats themselves.
• If you aren't struggling early on, save up crystals to try to get good orange or purple loot at the end of each run to further improve your build. For example, I saved up 500 crystals each run and spent it on the pistol shrine until I got a level 40 orange one that was perfect for my build. Do the same for whatever piece of gear you need to improve your class (and then don't forget to enchant it!)
• If you start to struggle, ignore loot and spend your crystals on the shrine buffs, again focusing on your build. I always purchased damage reduction and damage increase, and I always ignored stuff related to spells or dark magic because I don't use them
• Always, ALWAYS choose the Butt Stallion portal if that option is available after an encounter. She will give a random skill you've invested points into another 2 or 3 skill points that last for the entirety of your run. This is huge, as you can imagine, because you can get massive boosts to your existing skills from both your class mod and from Butt Stallion. Never pass up this opportunity
• Never, NEVER choose the Dragon Lord portal option. This forces you to choose another negative modifier, and with two options per encounter, there is literally never a reason to choose this option
• When you're forced to choose a Dragon Lord option in the beginning, there is never a reason to choose a harder option. Always choose the Easy option (or Medium, if it's between Medium or Hard)
• Just ignore the secondary objective every time. There is no need to complete it, and it will only increase the likelihood of dying, so don't ever bother with it

Hopefully those tips, the loot you've gotten and will get during your runs, and your by-now-optimized build will get you through all of the required runs to unlock Chaos Level 20 for this achievement.