First off, the achievement description is inaccurate, as you must complete the game in less than 25 minutes (not 30 minutes). This is a game design issue, not a problem with TA.
Second, unless you are extraordinarily awesome at this game, I highly recommend that you play through the entire game multiple times, meaning that you must defeat Master Sura. The reason for this is that two Chaos Arcana are super helpful in this speedrun. These are Phantom Brigade and Chaotic Rift. The first unleashes a swarm of knights that will attack the nearest enemies, which is helpful building your signature charge. The second is a dash that allows you to actually pass through enemies and their attacks, which has obvious advantages. I think it's the best dash in the game. Also, playing through the game will gave you a feel for the bosses and Sura, as well as the general attack patters of enemies. You'll also need to acquire enough gems to purchase the required relics, arcana, and outfit.
Third, I recommend the following order for fighting council members: Earth Lord Atlas, Frost Queen Freiya, and Flame Empress Zeal. This is a rotating order, so you'll either have to pay the dude to the left of the main dungeon portal to switch the order or die a few times until you get the order you want. This is up to you, but I found Earth Lord really challenging to fight third.
Fourth, here is my starting build: Grit cape for the defensive bonuses and the Pathfinder Map relic. This allows you to see the entire map at the start, which allows you to beeline directly toward the exit portal (mini boss fight). My arcana were Stone Shot, Chaos Rift, Rock n Roll, and Chaos Brigade. I acquired Evading Zephyr, Obsidian Cascade, and Airborne Slam on my run, and these were all middle of the road helpful. This is random, so take that for what it's worth.
In terms of relics, you'll not have a lot of gold to spend in the dungeon since your mission is to make the exit portal as quickly as possible. That said, you do have some wiggle room. If the merchant and/or cursed relic dude are close to the exit portal, it might be worth visiting them. The merchant was literally a lifesaver for me multiple times when I needed to heal.
Now I used the following relics, which again are all the luck of the draw: the cursed Volatile Gemstone (your signature charge builds but decays quicker and its damage is reduced; this is great for when you're unleashing an onslaught of attacks on multiple enemies, as you'll have no trouble filling the meter with the above load-out), Giant's Heart (increases your max health), Bladed Buckler (destroying enemy projectiles increases your signature charge), Amulet of Sundering (increases all damage dealt), Freezing Sprite Naya (freezes enemies or deals ice damage), the cursed Golden Armor of Envy (increases armor but also increases store prices except the health potions), and finally the Regenerative Inkwell. This last item is fantastic when paired with the Volatile Gemstone, as it allows you to use your signature attack to regenerate health. If you're lucky enough to pair both of these items with the Surefire Rocket (which keeps your signature charge from decaying and thus negates the downside of the Volatile Gemstone) you'll be damn near unstoppable.
Fifth, some practical advice in the dungeons:
- This goes without saying, but your main objective should always be to make the exit portal as quickly as possible. If you spend two minutes on each stage (and you should be able to do better than that), that puts you at 20 minutes total.
- This also goes without saying, but avoid enemies as much as possible. There are trap rooms where you must fight, but aside from these avoid fighting enemies at all costs.
- While you should be moving quickly, you don't need to rush so fast that you make careless mistakes. And, as I mentioned above, I highly recommend checking out the cursed merchant if he's close to the exit portal, and the same goes for the relic merchant, if for no other reason than making sure you can warp back to him to heal if need be.
- The first council member will attack three times before pausing. The second will attack four times, and the last will attack five times. Keep this in mind as you are dodging. You should have a good idea of what their attacks are by the time you start making your speedrun.
- Take your time with Sura. He attacks five times, then does one last dodge. If you try to bum rush him you will probably be killed very quickly, which sucks.
- In terms of attacks with your main arcana, if recommend launching the Rock n Roll and Chaos Brigade right away then following with your basic attack.
One last thing: you'll probably die quite a few times before you get the right combination of relics and useful arcana. I tried my speedrun about eight times before everything fell into place. You might find other arcana useful, but I'll leave that up to you. Good luck!