Here is the full list of all 42 Blood Bowl 3 achievements.
In 3 consecutive competition matches, concede no more than 1 Touchdown
Win a competition match with a Dark Elf team
Push 4 players into the crowd during a single competition match
Score 3 Touchdowns over 3 or less games in the same competition
Kill a player during a competition match
Complete a competition match with at least 1 Touchdown scored
Win a competition match with a Skaven team
Beat Varag Ghoul-Chewer by winning [The Outsiders] competition
Beat Kiroth Krakeneye by winning [The Pirate Crew] competition
Beat Withergrasp Doubledrool by winning [The Gifted] competition
Beat Kreek Rustgouger by winning [The Engineers] competition
Beat Josef Bugman by winning [The Gourmets] competition
Beat Griff Oberwald by winning [The Elite Division] competition
Complete a competition match with at least 4 Touchdowns scored
Make a single player gain 3 advancements
Improve 1 player to maximum level (six advancements)
Improve 6 players to maximum level (six advancements)
Score 6 Touchdowns over 3 or less games in the same competition
Score 12 Touchdowns over 3 or less games in the same competition
Spend 18 Star Player Points on the same player
Spend 38 Star Player Points on the same player
Successfully throw a team-mate during a competition match
Successfully throw a team-mate 2 times during a single competition match
Purchase 4 Team re-rolls for a single experienced team
Purchase 8 Team re-rolls for a single experienced team
Win a competition match with an Orc team
Win a competition match with a Human team
Win a competition match with a Dwarf team
Win a competition match with a Chaos Chosen team
Win a competition match with a Chaos Renegade team
Win a competition match with a Nurgle team
Win a competition match with an Old World Alliance team
Win a competition match with a Black Orc team
Win a competition match with an Imperial Nobility team
Win a competition match with an Elven Union team
Hurl a Fireball during a competition match
Turn a player into a frog during a competition match
Win a competition in which you played 4 or more matches
Hire a Star Player during a competition match
Hire 16 players in a single experienced team
Injure 4 players in a single competition match
Kill 3 players during a single competition match