Game Progression

First, let's talk about Tiering.  This new Epic Spirit weapon can be upgraded using the "Tier" system by using basic materials you will find while completing the main quest and farming various mobs.  To see what each tier gives you, select the weapon and scroll through the Upgrade Attribute section.  

You'll notice in the case of this bow that there are Five (V) tiers, and one final "End" tier.  This End upgrade turns this bow into a completely new weapon!  Although the base attack of this bow is only +60 Atk, all five of these tiers add another +180 for a total of +240 Atk, including some main stat bonuses and special modifiers like ignore defense and crit damage!

Let's select your weapon and tap on the Tier icon to bring up this interface.

The interface shows the materials you need for the next Tier and what bonuses you get for that upgrade.  In this case, the next tier will give me +45 Attack and +1 DEX.  From here you can also see where to obtain that item.  Tap on the material you want to find, then tap either the icon at the top of the item with the magnifying class on it, or the option "Inspect How to Obtain".  This shows you a list of each monster that drops it and where you can find them.  You can even tap on the blue arrow to travel right to that zone.

Even if you are missing materials you can just tap on the Level Up button anyway to bring up the buy menu to purchase this item from the exchange without even having to find an Exchange NPC.  This interface shows you how many are on the exchange and the cost to buy all of these items you are missing.  This allows you to quickly upgrade equipment without having to keep farming monsters or make trips to the exchange to buy materials one by one.

However, you will make much more money farming things you kill quickly, selling those materials on the exchange instead, then buying what you need with the funds.  Unlike other games, farming your own materials in this game is almost always a serious waste of time!  Focus on making the most zeny and use that zeny to bankroll these upgrades.  You will progress much faster and get to things that make you several million zeny a day in no time!

For more on Upgrading Equipment read up on Equipment Systems though I will cover more features as they are unlocked and/or become relevant to your progression.

Most of these things give you a bonus when the item first Drops (such as cards), or when it is first crafted (such as on headwear).  You also get an additional bonus if that item is deposited into your adventure handbook.  You'll want to fill your handbook with as much stuff as possible to pump up your stats!

You can remove any item deposited from your handbook at any time without any fees.  The deposit bonus will go away until you deposit it back into your handbook.  Keep this in mind if you find yourself carrying a lot of things you aren't actively using anymore that you may want to put back into your handbook.

Again, you won't have to worry much about these bonuses and collections yet, but somewhere around level 80 you will probably come back to this and start hunting down very cheap upgrades to start boosting your attack/mattack.

Fore more details on this system read up on Adventure Handbook.

This is a cheap way to add attack to weapons and accessories early on.  Other slots add defense but when you're starting out defense won't help you farm better so ignore that for now.  When you have the spare zeny feel free to upgrade your weapon and accessory slots for more damage.  Beware that the One-tap Strengthen button will spend all of your zeny to upgrade that slot as far as it can!   Don't press this if you don't have the spare zeny because this gets expensive the higher you go and can bankrupt you.

The quest will unlock all four of them.  You can access your mercenaries by clicking More and selecting Mercenary Cat.

These cats will be summoned for an entire week and will disappear once time expires.  You can re-summon them anytime you want for a 10k zeny per day, or using Mercenary Coupons.  These coupons are given away frequently through daily mission board quests that you will unlock soon so don't stress about spending a bunch of zeny on them, you will probably have more of these tickets than you know what to do with in no time.

These cats also have levels and skills that can be unlocked and improved.  I highly suggest working on Goro, the healing cast first.  This cat heals, and with upgrades buffs your defenses, gives you an SP regen buff, and even revives you if you die without messing up your auto farm.  This cat is by far the most useful of the bunch!

Rather than go into detail here I encourage you to read up on Cat Mercenaries to learn about how to unlock these skills and understand more about how the mercenary cat system works as there's too much to cover here.  The sustain they give you while farming is very useful.

Pet Adventure allows you to send pets out to gather materials from a zone or monster of your choice.  This can be a good way to farm monsters that are rough to farm due to spawns or scarcity that offer a good card such as the Minorous Card.  Each time you do this you spend 60 minutes of combat time.  Make sure you really need the thing you're farming otherwise you're just wasting combat time with this feature.

Pet Handbook shows all pets in the game.  You'll notice there are even higher tiered pets that are created by merging multiple pets together.  Use this handbook to determine which pets to tame and level in order to access higher tiered pets such as Osiris.

Pet Labor lets you assign pets to various facilities to generate free stuff over time.  For example, the item shop sometimes gives you experience potions, cuisines, and monster materials.  Only one facility is unlocked at first but others will unlock as requirements are met.  You can also only assign pets to two facilities are first but this limit will raise as you increase your adventure rank and buy passive that raise the limit.

Many monsters can become pets but each pet has a unique item used to tame them.  Although one item is enough to try to catch it, more increase that chance which can be raised to 100%.  These materials are either bought off the exchange, drop from the level 50 instance Endless Tower (ET), or can be exchanged using Colorful Shells obtained from pet adventure's.

For more on this system read up on Pets to learn more.  The Pet Catching Table has a list of tamable pets, items needed for taming, and quantity required for 100% success rate.  You'll find that you can tame most of the tier 1 pets for under 200k these days and some have passives that buff you such as ignore defense.