Preface

It's hard to provide a good walkthrough for Rogue Dungeon because the game is highly random and also skill-based. I know plenty of people who have take 10-20 tries to unlock 2x mode their first time. But a skilled player can usually beat 1x mode on a new game file their first run. See an example on YouTube.

Due to the nature of the game, this walkthrough will focus on the things you can control. You will need to learn how to make choices for your equipment and skills and how to fight enemies effectively.

First Dungeon

Your first foray into the dungeon might seem challenging if you're unfamiliar with the controls, but keep going and they will start to feel more natural.

Skill Selection

For your first run as Warrior, you should focus on a few things: efficiently killing enemies and choosing the right skills. For skill and weapon selection, you should focus on high-damage weapons and Crusher skills. The Warrior's spinning slash has a fixed cooldown and deals the same damage as a normal attack, so you can maximize the skill with a strong, slow weapon. If you are already focusing on strong, slow weapons then you should select other skills to maximize that: Painful Reminder, Cleave, and Slow But Strong are all incredible skills. If Crusher isn't available, Scholar and Athletics skills are both also effective. When choosing stats, focus on str, life and speed. Always get "Spinning Slash" (SS) at L5.

Item Selection

When choosing items, forget about DPS. You're not going to need it. You want to one-shot enemies as much as possible. The "+X% DPS" estimations on weapons aren't as important as your actual damage per hit in this build. In general, I weight damage at least 2x higher than dps. Choose a 10/1200 weapon over a 6/500 weapon even though the "dps" is higher in the second case.

Playstyle

Keep each of the following in mind as you play

Spinning Slash begins AND ends above your character. It can hit an enemy twice if the enemy's hitbox is in both parts of the slash (directly above you).

Try to fight enemies one-by-one. Move forward slowly to avoid agroing too many at once.

Your weapon cooldown resets even while you're moving. After attacking or killing one enemy, retreat away for a moment to let your attack recover before re-engaging. Most enemy attacks are faster than yours.

Identify areas where you can effectively kite enemies. Spinning slash can hit up to 4 times if you use it right, and it's range is slightly longer than most enemy attack range. When an area is challenging, skirmish only when SS is ready, approach the enemy pack from below, deal your damage from the edge and retreat.

Fully clear each level. There are so many unlockables on 1x difficutly that going far is much more important than going fast.

Save healing shrines and healing potions for when you really need them.

If you die, don't waste gemstones resurrecting - those will be more valuable later unless you plan on stocking up using In App Purchases (then go for it).

Floors

The key floors to reach are 8 (Shattered Blade Relic), 11 (Rogue class), 15 (Shielding Amulet) AND 17 (Unlock 2x mode). When faced with almost certain death, consider spending your remaining shards in the Boosts shop on a heroic potion to make it one more level and pick up the unlockable.

1. Fight your way through each room. Prioritize killing healers first. Goblins sometimes swarm in large numbers. If there are more than a few, retreat back while waiting on SS. Use corners for brief relief from knife throwers.
2. Grab the 'Crow' pet. Explore North, then South, then finally East. Don't forget to equip items as you find them. Optionally, by level 3 if you're unhappy with your items and skill selections, you can consider restarting. Try to kill the boss without getting hit. Retreat backward as he winds up his attack. If you get hit he'll take a large chunk of health. Practice barely entering his attack range to trigger an attack, step back to dodge, then move in for 2 seconds of safe damage. The Golden Hammer is almost always an upgrade over your current weapon.
3. Work your way through all of the mudmen slowly. They move very slowly, so use that to your advantage. The exit crystal tends to spawn towards the south of the level.
4. The ice cave map is small and almost impossible to kite in. Progress very slowly to minimize agro. Wait for SS before moving forward.
5. The desert is the most dangerous level you've encountered so far. Brown cacti shoot high-damage spikes but have low hp so try to strafe around as you approach them with SS. A round of Attack + SS is almost always enough to kill one. Watch out for ogres who fight like the Level 2 boss (retreat away when they wind up). Make sure to kill them though, because they somtimes drop a "Big Club" which has extremely high damage.
6. Watch out for flying skulls and scorpiars. Enemies on this floor have high move speed. If you're feeling overwhelmed resist the urge to run into unexplored territory. Many deaths happen here when you jump "out of the frying pan and into the fire" by running into a new groups of enemies.
7. Inside the tower, you'll encounter a similar set of enemies but with a bit more space to maneuver. The Griffon boss has similar dynamics as previous bosses. Get used to timing his attacks to minimize the damage you take by retreating back during his wind-up.
8. The plants on this level are very tough but immobile. Work slowly through with attack+SS. Avoid the tempation to try to land SS on multiple enemies - stay safe a kill them one-at-a-time. These plants have a pretty long attack range, so every skirmish is going to result in you taking damage. This level doesn't usually have a lot of healing. Use healing potions to keep your life up if you don't find enough hearts & shrines. Open your inventory, then choose the 'Boosts' menu and buy 1-2 healing potions for 80 shards each. If you're still running low on life, the exit is on the far east side of the level and you can get there without fighting too many enemies. Make sure to reach floor 8 where you will find your first new Relic.
9. Pick up the Shattered Blade. The Scoundrels on this floor are fast and powerful, but you should have enough damage to kill most of them with your spinning slash.
10. The Mad Cubes here have fast attack speeds - avoid prolonged fights and instead dance in and out of combat as you wait on weapon cooldowns.
11. Werewolves don't usually cause any more problems than mad cubes - just watch out for their long agro range and fast movement speed to avoid being swarmed. The Rogue Class is likely to spawn on this level so unlock that if you can (sometimes it won't show up til 12, 13 or 14).
12. Ghosts are even scarier than werewolves with higher movement speed. If you've found decent items by now however they will go down quickly because their life isn't that high.
13. Nothing special here. The Maw enemies are tough but nothing you can't handle.
14. Again, nothing special to worry about. Snowmen have surprisingly high combat capabilities but they're easy to take down one-by-one using the same tactics as you've been using.
15. Pick up the Shielding Amulet. Reapers are the hardest enemies you've encountered so far, but if you made it this far then you'll probably be equipped well enough to take them out.
16. Final boss. He has two attacks: a melee slash and a powerful ranged magic attack. The melee attack is unavoidable, but the magic attack can be dodged. His magic is cast every 5 seconds or so and has a small wind-up. When you see his arm raise, start strafing around and the bolt should miss you. If you win this battle, the Greatsword drop will probably be an upgrade. Pass through the crystal to unlock 2x mode.
17. You're back in the Mine, but this time enemies are MUCH stronger. You probably won't make it much further. If you have any open potion slots still, buy a Max Life potion from the Boosts shop and save it for the next run. If you gain any levels, hope for Scholar > Devoted Researcher for a small bonus to your end-of-run shards. At this point don't waste any precious healing potions. You'll want those potions for the next run. The next unlockable isn't available until floor 22 and isn't really that good yet (Mage Class) so unless you're rolling around with an absurdly strong purple weapon, don't worry about losing.

After you die, from the main menu go to 'Relics and Upgrades'. Spend your shards in the Relics tab to upgrade Wicked Tome, Shattered Blade and Shielding Amulet. If you have >5,000 shards you can consider buying a few ranks of Boots of Speed. Don't spend money on Brilliant Bauble yet. Spend your gold in the Upgrades menu to increase your Shard Gain per run. If you somehow ended up with 200 gemstones, go to the Bonuses menu and exchange 200 gemstones for 5 Prisma which you can spend on additional upgrades.

2x Mode

After unlocking 2x mode, your next goal should be to reach 2x floor 6. Follow the same tactics as before with the Warrior class. On floor 2 you'll find the Wolf pet (my favorite) and on floor 6 you can find the Defense Gem relic. If you saved up a few potions including Max Life potions, this should be very doable. The biggest challenge might be floor 1. With just a Club to start with, one or two healers can really ruin your day because it will be hard to out-damage their healing until you find a better weapon.