Companions, or Legendary Memories, are items that you can equip that will give you a summon ability during your runs. To get them, you will need to cultivate Nectar which you can then give to various NPCs to increase your relationship level with them. After giving them six Nectars, each NPC will reward you with a companion.
How to equip companions
To equip your companion, you will have to visit the display case in the courtyard at the start of the race, and you cannot change it during a race.
It is possible to upgrade your companions, getting more uses from them during a race, by using Ambrosia.
All companions
Antos
You can get Antos by giving enough Nectar to Achilles. Your summon inflicts 1500 damage to two enemies. Antos will have five uses per race at maximum rank.
Battie
You can get Battie by giving enough Nectar to Megaera. Your summon inflicts 2500 damage multiple times to enemies in front of you. Battie will have five uses per race at maximum rank.
Fidi
You can get Fidi by giving enough Nectar to carried. Your summon fires petrifying blows at enemies for 15 seconds. Each shot inflicts 70 damage. Fidi will have five uses per race at maximum rank.
death
You can get Death by giving enough Nectar to Thanatos. Your summon deals 3500 damage in an area in front of you after a short delay. Death will have five uses per race at maximum rank.
Rib
You can get ribs by giving enough nectar to Skelly. Your summon distracts enemies in an area, preventing them from attacking you for a short time. The rib will have five uses per stroke at the maximum rank.
Shady
You can get Shady by giving enough Nectar to sisyphus. Your summon deals 1000 damage in an area and causes you to lose health, darkness, and gold. Shady will have five uses per race at max rank.