The Alchemist is a class which optimizes Potion Creation and Homunculus, as well as various other potion-related skills. They are a class which work for the benefit of their friends and strike terror into the hearts of their foes (armor).
Changing into an Alchemist from a Merchant requires the player to complete a number of tasks:
Item Collection
Written Test
Transformation Experiment
After completing these tests, the player will be transformed into an Alchemist.
Builds
Cart Revolution Build
STR: 70-90
AGI: 30-50
VIT: 70-90
INT: 1+
DEX: 50
LUK: 20-40
This build is centered around the Cart Revolution skill for AoEing groups of monsters at once. ASPD does help Cart Revolution spam rate, especially when pushing monsters against walls. Mammonite still provides high single target damage.
AGI Build
STR: 70-90
AGI: 80-99
VIT: 50-70
INT: 1
DEX: 40-60
LUK: 20-40
The AGI build is is usually recommended for newer players without funds. They have high ASPD and FLEE for quick single target killing, so it uses minimal HP / SP Healing Items. Their main method of attack is melee-ing single monsters, and sometimes utilize autocast gear. Alchemists do not have skills that increase flee rate (like a Thief's Improve Dodge, so it is recommended to use at least SOME sort of FLEE gear (such as Falcon Muffler or Whisper carded garment).
DEX: 30-50 (for leveling up until getting a Homunculus)
LUK: 20-40
Acid Terror/Bomb build
STR: 80-90
AGI: 1+
VIT: 70-90
INT: 1
DEX: 30-50
LUK: 20-40
This build is for rich players with a lot of funds that want to level faster.
Brewer
STR: 1
AGI: 1
VIT: 1
INT: 46
DEX: 90
LUK: 94
This has one of the highest success rates for Potion Creation, but requires a lot of leeching. LUK may be preferable to DEX as most Gypsies and Minstrels have high DEX but do not have any LUK. Thus, when Marionette Control is used with this build, the Alchemist will receive a significant boost in DEX from the Gypsy or Minstrel, and the Alchemist's own LUK will further increase success rates for brewing.
This stat build is NOT recommended if you have Marionette Control available to you to boost stats. If you are using Marionette Control you can reasonably expect a +45 boost to DEX for most builds with 90 DEX.
If you have access to Gypsy or Minstrel on your server you really shouldn't even be looking at the stat builds for the Alchemist as the job level of 70 for the biochemist greatly increases the success rate for potion creation.
Eden Group Equipment is free and a great place to start for gear to use. The One Handed Sword is a good weapon and generally a good choice for an Alchemist and their future classes' use.
It is recommended to look at the Equipment recommendations for the Third Class job to see what equipment to strive for, rather than to spend a lot of money on a piece of equipment that will not be used in the future as a third class. However, some equipment may have a high level requirement, or are transcendent only.
Weapons
After considering what requirement skills have (some skills can only be used with certain weapon types), the Weapon Search tool within the iRO Wiki DB site is very helpful. Generally, for physical classes (both melee and ranged), something with high ATK is best. For magic classes, something with high MATK is best.
The weapon used is primarily based upon one's build. For example, an Alchemist prioritizing AGI and ASPD should generally use Swords. Those preferring to maximize damage are better suited with Axes. The following is a listing of the most common weapons and why they are beneficial:
Common Weapons
Swords are some of the most common among Alchemists primarily due to the relatively low ASPD delay as well as their moderate ATK. However, the player will be unable to benefit from having a Blacksmith partner, which is relatively rare. Also, because of the skill Axe Mastery it is evident that one will be able to bring out optimal damage from an Axe. However, Axes have a large ASPD delay, which means they swing slow but hard. On the positive side, players using Axes can not only benefit from Axe Mastery but also a Blacksmith partner.
Saber [3]: A common weapon generally used with damage cards. (ATK 115)
Nagan: A sword that deals extra damage with Level 5 Double Attack and it's rather light, but it lacks of Card Slots. (ATK 120)
Two-handed Axe: The best choice for elemental weapons because they have the highest ATK among weapons forgable by Blacksmiths. However, they lack of Card Slots, so a study is required. (ATK 185)
The Homunculus is a pet that kills, supports, and does everything for its master. An Embryo, from which a Homunculus will be born, can be created via Prepare Potion with the following materials purchasable from the Al de Baran Material Seller, in the Alchemist guild alde_alche35179:
Once an Embryo has been created (or purchased from another player), use the skill Call Homunculus to receive 1 of 4 types of Homunculus. The Homunculus received is random, and each type has two sprite variations. Much like Cute Pets, Homunculi need to be fed or they will leave their owner:
Throws a Bottle Grenade at the ground to create a 3x3 cell fire, dealing 60~300% Fire property physical damage every 0.5 seconds to enemies that step into it. May break their weapons by chance.
Snake Head [1] or 
Chick Hat
Musketeer Hat
CD in Mouth
Heroic Backpack
Ring of Flamelord
Medal of Honor or 
Bakonawa Agimat Tattoo
Nagan: A sword that deals extra damage with Level 5 Double Attack and it's rather light, but it lacks of Card Slots. (ATK 120)
Two-handed Axe: The best choice for elemental weapons because they have the highest ATK among weapons forgable by Blacksmiths. However, they lack of Card Slots, so a study is required. (ATK 185)
Light Epsilon: An axe that allows the use of Level 3 Heal. (ATK 180, +3% damage to Demon, Holy property)
Fireblend: A sword that allows to use Lv. 3 Fire Bolt. (ATK 100, Fire property, may autocast Lv. 3 Fire Bolt while attacking)
Ice Falchion: A sword that allows to use Lv. 3 Cold Bolt. (ATK 100, Water property, may autocast Lv. 3 Cold Bolt while attacking)
Tomahawk: An axe that allows to use Lv. 1 Tomahawk Throwing. (ATK 165, Wind property)
.png){kind=small}
.png){kind=small}
.png){kind=small}
