A list of achievements that rewards you honor medals and a board showing what you achieved with a medal(non-repeatables) or ribbon(repeatables). The achievement board would show the amount of times you achieved each repeatable category.

Another idea is for each achievement to unlock you a title that can be used under or above your nickname in the forums.

Daily achievements: each achievement rewards you 1 honor medal (repeatable)

• 7 ships sunk in a single match
  
• 10 ships sunk in a single match
  
• 12 ships sunk in a single match
  
• 15,000 CREDITS in a single match
  
• 20,000 CREDITS in a single match
  
• 30,000 CREDITS in a single match
  
• 200,000 ATTACK in a single match
  
• 250,000 ATTACK in a single match
  
• 300,000 ATTACK in a single match
• 3 consecutive wins in a single log-in
• 5 consecutive wins in a single log-in 
• 7 consecutive wins in a single log-in
• Survived 5 consecutive matches in a single log-in

Weekly achievements: each achievement rewards you 5 honor medals (repeatable)

• MDP Winning Point top 30
• Enemy Sunk Point top 30
• Credit Earning Point top 30

Ships sunk: each step rewards you 10 honor medals (non-repeatable)

• Sunk 50 FFs --> 100 FFs --> 200 FFs --> 350 FFs --> 600 FFs
• Sunk 50 DDs --> 100 DDs --> 200 DDs --> 350 DDs --> 600 DDs
• Sunk 75 CLs -->150 CLs -->350 CLs --> 600 CLs --> 900 CLs
• Sunk 75 CAs -->150 CAs -->350 CAs --> 600 CAs --> 900 CAs
• Sunk 500 BBs -->1000 BBs --> 2000 BBs --> 5000 BBs --> 10000 BBs
• Sunk 150 CVs -->300 CVs --> 600 CVs -->  1500 CVs --> 3000 CVs
• Sunk 250 SSs -->500 SSs --> 1000 SSs --> 2500 SSs --> 5000 SSs

Activity: each step rewards you 5 honor medals (non-repeatable)

• 2,000 battles played --> 4,000 --> 6,000 --> 8,000 --> 10,000 battles played
• 1,200 battles won ---> 2,400 ---> 3,600 ---> 4,800 ---> 6,000 battles won
• Logged in at least once a day for 200 days --> 300 --> 400 --> 500 days

End-game achievements: each achievement rewards you 5 honor medals (non-repeatable)

• Reached the Hall of Fame
• Reached level 120 with an BB BO
• Reached level 120 with an CV BO
• Reached level 120 with an SS BO
• Reached level 120 with an USN BO
• Reached level 120 with an RN BO
• Reached level 120 with an IJN BO
• Reached level 120 with an KM BO
• Reached level 120 with an MN BO
• Reached level 120 with an SN BO
• Reached level 120 with an RM BO

Olives: (repeatable)  

• Spent 500 olives in a single transaction: 1 medal
• Spent 1000 olives in a single transaction: 3 medals
• Spent 2000 olives in a single transaction: 10 medals

Already suggested achievement systems:

Monthly events and achievements

"Achievement Unlocked" concept