Here is the full list of all 20 Risk achievements worth 1,000 gamerscore. It takes around 15-20 hours to unlock all of the achievements on Xbox One.
Win a game having lost no more than 3 territories.
Win a game in which you were last in the player order
Reach turn 4 without losing a territory
Win a game in 10 turns or less
Win 3 games in a row
Complete a game with at least 2 local human players
Conquer 100 territories with one defender in
Attack 100 territories with at least twice as many troops as the defender has
Deploy 20 troops in one turn
Spend 5 stars in a single purchase of troops
Reach turn 5 without losing a battle as the attacker
Conquer 7 or more territories in one turn
Attack with 10 or more troops
Conquer a territory taking no casualties
Control a continent by the end of your 1st turn
Eliminate 50 players
Get promoted to the Major's League
Get promoted to the Colonel's League
Get promoted to the General's League
Win the General's League