Here is the full list of all 37 Forge and Fight! achievements.
Win a game
Win a game after losing the first two rounds
Build your first weapon
Build 25 weapons
Build 100 weapons
Build 1000 weapons
Eliminate 10 enemies
Eliminate 100 enemies
Eliminate 1000 enemies
Eliminate 5000 enemies
Reroll 10 times while drafting
Reroll 100 times while drafting
Reroll 1000 times while drafting
Unlock the full Tod's Trapper Gear Set
Unlock the full Billabonk Set
Unlock the full Damascus Set
Unlock the full Defendr Set
Unlock the full Zap! Set
Unlock the full Hot Rod's Hot Rods Set
Unlock the full Sharp Set
Unlock the full Blunt Set
Unlock the full Mechanical Set
Unlock the full Rifle Set
Acquire your first cosmetic
Create your first outfit
Draft 6 Bricks
Start or join a party with another player
Get a 3 Multi-elimination
Get a 5 Multi-elimination
Eliminate an enemy using fire
Eliminate an enemy using electricity
Eliminate an enemy by using environmental hazards
Run really fast
Hit an enemy from really far away
Secret achievement