Here is the full list of all 13 Forge achievements.
Complete the tutorial!
Kill all bots on medium
Kill all bots on easy
Claimed the first kill in a match
Kill all bots on hard
Deal 10,000 damage to enemies
Deal 100,000 damage to enemies
Heal team mates from 50,000 points of damage
Heal team mates from 500,000 points of damage
Protect team mates from 5,000 points of damage
Protect team mates from 50,000 points of damage
Capture the relic 100 times
Capture the relic 5,000 times