Here is the full list of all 43 Cardfight!! Vanguard Dear Days achievements.
Acquired all Trophies
Had your first cardfight.
Watched the ending
Completed Rasen Ichidoji's story
Completed Yu-yu Kondo's story
Completed Danji Momoyama's story
Completed Tohya Ebata's story
Won 10 fights with Dragon Empire
Won 10 fights with Dark States
Won 10 fights with Brandt Gate
Won 10 fights with Keter Sanctuary
Won 10 fights with Stoicheia
Won 10 fights with Lyrical Monasterio
Won 100 times with a nation
Fought in World Fight for the first time
In-rank class went up for the first time
Became Bronze Rank
Became Silver Rank
Became Gold Rank
Became Platinum Rank
Became Master Rank
Won 20 times at Master Rank
Fought 50 times in total
Fought 200 times in total
Fought 500 times in total
Fought in CPU Fight for the first time
Fought all characters in CPU Fight
Deconstructed a card for the first time
Crafted a card for the first time
Bought any item in a shop for the first time
Acquired all cards
Acquired all sleeves
Acquired all playmats
Acquired all cards and supplies
Rode on a grade 3 premium card
Performed a Persona Ride
Performed an overDress
Got the over trigger in a fight
Won a fight with a card link attack
Got 3 triggers in a row during a battle
Won a fight at 3 or less damage
Attacked 6 or more times in a turn
Performed perfect guard 3 times in a turn