TEXT: Animal Companion Leveling Guide
  Companion Rules
  In Combat
  Your companion acts on their own initiative unless they are
  being used as a mount, in which case they act on their own. If
  you fall unconscious, your companion will prioritize
  defending you.
  Communication
  While your companion does not necessarily understand any
  language you speak, it will follow simple commands and you
  are able to instruct it to perform simple tasks. Your
  Companion is completely loyal to you and will do it's best to
  be helpful as possible.
  Barding Armor
  Barding armor is described in the Equipment Section of the
  PHB. Barding for medium and small creatures costs twice as
  much as normal armor and weighs the same amount.
  Magic Items
  While magic items for animal companions are somewhat
  more rare, they are not unheard of. In general, magical armor
  is fairly easy to convert into barding armor, although it will
  require the work of an experiencde blacksmith. While
  traditional magic weapons such as swords and bows are not
  something companions are equipped to handle, there are
  other ways to magically enhance their attacks, such as wraps,
  gauntlets, claw extenders etc.
  Companion Options
  Level
  Proficiency Bonus
  Features
  3rd
  +2
  Natural Talents
  5th
  +3
  True Ally
  7th
  +3
  Worldly Veteran
  11th
  +4
  Heratage Traits
  15th
  +5
  Grizzled Defender
  18th
  +6
  Transcendence
  Hit Points
  Companion Hit points are calculated by taking the average of
  the creature's HP (from their stat block) + the player's level
  * your companion's CON mod
  Proficiencies
  Armor: All barding armor
  Weapons: Natural Weapons
  Tools: None
  Saving Throws: Choose from Strength, Dexterity, or
  Constitution
  Skills: None
  Options
  At each Feature level, you have the option to have your
  companion take the given ability or to increase one Ability
  Score of your choice by 2, or two Ability Scores of your choice
  by 1. As normal, you can't increase an ability score above 20
  by Ability Score increases.
  Natural Traits
  At 3nd level, your companion understands a little bit more
  about the battlefield. Choose one of the following Traits to
  learn.
  Defensive. Your Companion gains +1 AC and an
  additional 1 hp for each level you have
  Offensive. Your Companion's attacks have +2 to hit and
  damage rolls
  Protective. When a creature your companion can see
  attacks a target other than them that is within 5 feet of
  them, they can use their reaction to impose disadvantage
  on the Attack roll.
  Aggressive. When your companion takes the attack
  action, they can make one additional attack as a bonus
  action. They do not add their ability score modifier to the
  damage for this attack.
  True Ally
  At 5th level, your companion becomes more loyal to you and
  your friends than ever, even in the event of your death.
  Choose one of the following options.
  Grief. If you or one of your allies fall unconscious, your
  companion can stabilize them, making a DC 10 Survival
  or Medicine check. How your companion specifically
  stabilizes a creature is up to the narrative. As examples,
  your companion may lick your wounds or attempt to move
  a contorted unconscious body into a more natural
  position.
  Rage. If you or one of your allies fall unconscious, your
  companion can immediately move up to their movement
  and take the attack action against a creature.
  Worldly Veteran
  at 7th level, your companion has had time to mature and
  practice what it knows. It gains proficiency in 3 skills and 1
  saving throw of your choice.
  
  Heritage Traits
  At 11th level, your companion becomes even more of a
  manifestation of their species. The trait they gain is based off
  of the type of creature they are.
  Reptillian. Your companion gains an elemental breath
  attack of your choice (consult the Dragonborn Race for
  details on saving throws and area of effect). The Breath
  attack damage is 3d6 and increases by a d6 when you
  reach 15th and 18th level. Once it uses it's breath weapon,
  at the top of each of it's turns, roll a d6. on a 5 or 6, it
  regains it's breath weapon. It regains it normally on a
  short or long rest.
  Mamillion. If the your companion moves at least 20 feet
  straight toward a target and then hits it with an attack on
  the same turn, the target takes an extra damage dice from
  the attack. If the target is a creature, it must succeed on a
  DC 13 Strength saving throw or be knocked prone. The
  damage increases by another damage dice at 15th and
  18th level.
  Arachnid. Your companion's attacks now deal 3d4 poison
  damage in addition to their normal damage. The damage
  increases by a d4 when you reach 15th and 18th level.
  Bird. Your compaion can now attack twice when taking
  the attack action, and doesn't provoke opportunity attacks
  when it flies out of an enemy's reach.
  Crustacian. Your compainion gains +2 AC and has
  advantage on saving throws against spells, and any
  creature making a spell attack against it has disadvantage
  on the attack roll.
  Aquatic. Your companion has advantage on attack rolls
  against any creature that doesn't have all it's hit points
  Grizzled Defender
  At 15th level, your companion is used to combat situations.
  Choose one of the following options.
  Relentless. Your companion can keep fighting despite
  grievous wounds. If they drop to 0 Hit Points and don't die
  outright, they can make a DC 10 Constitution saving
  throw. If they succeed, they drop to 1 hit point instead. If
  they fail, they cannot use this ability again until they finish
  a short or long rest.
  Carrier. Your companion can now carry and or drag one
  creature one size larger than itself or two creatures its
  size or smaller without halving it's movement. Its base
  speed (includes climbing or swimming if applicable) also
  increases by 10 ft.
  Transcendence
  At 18th level, your companion has transcended its natural
  being. Choose one of the following options.
  Sentience. Your companion can now speak telepathically
  to any creature it can see within 60 feet of it. Your
  companion doesn't need to share a language with the
  creature for it to understand the telepathic messages, but
  the creature must be able to understand at least one
  language or be telepathic itself.
  Etherial. Your companion can now use a bonus action to
  magically teleport, along with any equipment it is wearing
  or carrying, up to 60 ft to an unoccupied space it can see.
  Resistant. Your companion is now resistant to all
  damage, excluding Psycic damage.
  Magical. Your companion gains 4 cantrips of your choice
  from any spell list that it can cast at will. Damage is based
  on your level.
  Rules by u/Onomonopedia
  
SOURCE: textdata/thevault/Dungeons & Dragons [multi]/5th Edition (5e)/3rd Party/Homebrew/Animal Companion Leveling Guide.pdf