Here is the full list of all 10 LONN achievements.
Use the punching bag
Acquire the gloves in Lunas Hideout
Get into a fight and knockout a city resident
Pet the dog
Get out of the Wux-N Laboratory
Kill a Wux-N by launching an object with your glove
Survive the bank assault
Kill a Bomb Bot by luring it into a trip mine
Unlock all weapon blueprints at Luckys
Escape Megalo's mind control