Log-in to Phantasy Star Online 2 on Steam. That's it.

Rewards:
720: Headcrab (Emote) | Half-Life








Additional Log-in Rewards:

• EXP Earned +50% (x5)
  
• Rare Drop Rate +50% (x5)
  
• Meseta Earned +50% (x5)
  
• Half Scape Doll (x5)
  
• Unit "Back / Fresh Aura" (x1)

Complete any quest once on Normal/Casual difficulty or higher.

Rewards:
Pyro's Gas Mask (Hairstyle) x2 | Team Fortress 2

Complete any quest once on Hard/Hardcore difficulty or higher.

Rewards:
720: Headcrab (Emote) | Half-Life

Complete any quest once on Very Hard difficulty or higher.

Rewards:
Alyx Replica (Outfit: Female) | Half-Life: Alyx







Alyx's Hair (Hairstyle) x2 | Half-Life: Alyx

Complete any quest once on Super Hard difficulty or higher.

Rewards:
HEV Suit (Outfit: Male) | Half-Life 2

Updated/Edit:
I seem to have received these rewards randomly, so I think you receive these rewards by completing all the difficulties above or play the game long enough to receive these rewards:

The Rewards:
Evolution Device: Wheatley | Portal 2







TF2 Minigun (Weapon Camo) | Team Fortress 2







L4D Frying Pan (Weapon Camo) | Left 4 Dead







Crowbar (Weapon Camo) | Half-Life

The Rewards can be claimed at:

• Arks Missions
  
• Gate Area's Title Counter
  
• Log-in Rewards

You can find the source here on PSO2 Steam Updates or on their Official PSO2 Website.
Steam Version
PSO2 Version[pso2.com]