Wizard of Legend

A much easier way to get this achievement is to buy the Cursed relic "Rules of Contingency" from the shop in top left of the lobby. (only shows up after beating the game once)

combine that with the arcanas "Bouncing Bubble" and signature "Volt Pinball". For outfit, it doesn't really matter, but I used Tempo.

For your normal relic use the "Pathfinder's Map", I was able to get a 5:51 run with that setup on my first try.

if you're struggling use either "Tea of Mercy" or "Scissors of Vitality" instead of the Map, and while you're playing buy some cursed relics and shop items that would help with total life, cool down reduction or resurrection. You will always hit and get hit 99 damage no matter what relics you pick up, so the downsides of most cursed relics will not affect you.

Just activate volt Pinball to shield you and spam bubbles, not much to explain for the strategy. For bosses just Dodge the first set of attacks and then you should be able to kill them on the first stun. Having the fire/ice boss as the last boss is preferable, as the earth boss is pretty annoying because the trees in the arena.

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!

This is a bit of extra tips on top of Bruin's and Cellar Attic's solution, on how I found it easiest to clear this, and get my second and third chaos arcana in a row.

Wizard Robe: (Pace could also be good, Evasion / Run Speed)
Tempo: Decrease Cooldowns (-12%), Increase run speed (+8%)
Main thing is the decreased cooldowns, the run speed is just a bonus.

Starting Relics:
Rules of Contingency: Chaos (Top left shop after defeating Master Sura, you can only buy one per run)
Pathfinder's Map: Standard : Pool 3 (Permanently reveals the map)

Buying/Acquiring Relics:
There are only a few things that you should really care about when choosing relics.
Revival : to give you a second chance.
Damage Avoidance : (Evasion/Parry) to reduce any attacks while you don't have Evading Zephyr up.
Extra attacks : (Procs/Attack Speed) to increase your damage output.
Cooldown reduction : to reduce the amount of time you don't have Evading Zephyr available.
It should be pretty clear what relics will help you considering that attacks will always do 99 damage.

Starting Arcana:
Severing Slash : Basic : Pool 4 (Extremely fast attacks with decent AoE, 297 damage every half a second or so, you should spam the attack button instead of holding it because of the charge final attack)
Wave Front : Dash : Pool 3 (Short shield with decent range and massive damage, 693 damage with full damage)
Volt Pinball : Signature : Pool 5 (Circling projectiles that bounce to other enemies on hit, amazing damage)
Evading Zephyr : Standard : Pool 5 (Evade all attacks for around 2.5 seconds while moving / using basic arcana, 6 second cooldown)

Buying/Acquiring Arcana:
Honestly its best to ignore most arcana, they will end up getting you hurt more than they will help. The only ones which are any good are aura type arcana which deal damage in an aura around you. Or those which hover in place for a moment and attack quickly.

Note on Pools:
For those trying to unlock these Arcana/Relics and can't find them... Arcana and Relics are sorted into 5 pools. After purchasing/unlocking half of the Arcana/Relic in a pool, you unlock the next one. Example: There are 17 Pool 1 Arcana, after unlocking 9 of them, Pool 2 Arcana will start appearing.

Strategy:
Regular Floors: Rush straight to the portal to the next floor unless there is a nearby shop, or you need health. I find it helpful to make sure Evading Zephyr is available in order to evade any possible damage whenever I am about to enter a room that may lock me in to fight enemies. That said, it isn't always necessary but it will be a lot safer. Upon reaching the portal, wait for all your cooldowns to reset. Activate the mini-boss, back away and wait a moment before using Volt Pinball. Just before the mini-boss is able to become damaged, activate Evading Zephyr. When it is able to be damaged use Wave Front to chunk the mini-boss, then just hit them with Severing Slash if they aren't dead yet.

Lightning Twins: I found them incredibly difficult to beat using Rules of Contingency if you play passively. Instead I found it much better to attack at the first opportunity using the regular combo (Volt Pinball, Evading Zephyr, Wave Front, Severing Slash). This should prevent them from doing as many erratic attacks which are difficult to dodge.

Other bosses: Honestly the best way to do these is to evade until either they have finished a combo or are using a skill where they are stuck in place. When they are in this position, activate Volt Pinball and Evading Zephyr before using Wave Front and then attacking with Severing Slash. This should kill any boss in a single Evading Zephyr.

Master Sura: Funnily enough, Sura is actually extremely weak to this strategy. For the first phase, just do the regular combo (Volt Pinball, Evading Zephyr, Wave Front, Severing Slash). His first phase will end almost instantly. When Master Sura is talking to you, WAIT while he chats, your cooldowns reset! When they are all back up, you can either evade his first five attacks (each element) and then attack when he is going to use his chaos attack, or you can just go straight into attacking him. The second time I used this strategy I ended up taking him down almost instantly in his second phase as well, and didn't even let him finish all of his elemental attacks.

An alternative if the solutions above don't work for you.

Equipment suggested (you need to beat the game once before)
Robe : Hope
Cursed relic : Rules of Contingency
Relic : Pathfinder's Map
Basic : Bouncing blaze
Dash : Circuit line
Standard : Whirling Wind Agent
Signature : Volt Pinball

Tips :
- Basically, protect youself with VoltPinball, and let your agents do the job and spam X on the remaining ennemis.
- Try to get another agent or revive relics if possible if the PNJ are on you way toward the exit of each map.
- For the bosses, summon the agents immediatly, as soon as possible then dash the first attacks. I've found the air boss the hardest to dodge, because he will kill you immediatly if you're catched.

Just to give you an idea of how I've beaten the last boss with this technique (go directly to 00:43s of the video) :

Courage, you'll get it !