Tumor Familiar (Ex)
Benefit: The alchemist creates a Diminutive or Tiny tumor on his body, usually on his back or stomach. As a standard action, the alchemist can have the tumor detach itself from his body as a separate creature vaguely resembling a kind of animal suitable for a familiar (bat, cat, and so on) and move about as if it were an independent creature. The tumor can reattach itself to the alchemist as a standard action. The tumor has all the abilities of the animal it resembles (for example, a batlike tumor can fly) and familiar abilities based on the alchemist’s caster level (though some familiar abilities may be useless to an alchemist). The tumor acts as the alchemist’s familiar whether attached or separated (providing a skill bonus, the Alertness feat, and so on). When attached to the alchemist, the tumor has fast healing 5. An alchemist’s extracts and mutagens are considered spells for the purposes of familiar abilities like share spells and deliver touch spells. If a tumor familiar is lost or dies, it can be replaced 1 week later through a specialized procedure that costs 200 gp per alchemist level. The ritual takes 8 hours to complete.
An Alchemist can obtain a http://www.d20pfsrd.com/classes/base-classes/alchemist/discoveries/paizo---alchemist-discoveries/tumor-familiar-exTumor Familiar. There's also the feat Improved Familiar, which is accompanied by a table which lists Arcane Spellcaster Level in one of the columns and has the prerequisite:
Improved Familiar
This feat allows you to acquire a powerful familiar, but only when you could normally acquire a new familiar.
Prerequisites Prerequisites: Ability to acquire a new familiar, compatible alignment, sufficiently high level (see below).
Benefitsufficiently high level (see below).: When choosing a familiar, the creatures listed here are also available to you. You may choose a familiar with an alignment up to one step away on each alignment axis (lawful through chaotic, good through evil).
Improved familiars otherwise use the rules for regular familiars, with two exceptions: if the creature's type is something other than animal, its type does not change; and improved familiars do not gain the ability to speak with other creatures of their kind (although many of them already have the ability to communicate).
http://www.d20pfsrd.com/feats/general-feats/improved-familiar
http://paizo.com/pathfinderRPG/prd/feats.html#improved-familiar
In the accompanying table, one of the columns is Arcane Spellcaster Level.
Can the alchemist class fulfill the sufficiently high level prerequisite and take Improved Familiar?