After doing the tutorial section you will arrive in Lestallum. The main concept of this mode is to do quests and gain "KW" power. To do quests talk to Monica and select the mission depending on the difficulty and reward you wish. Early game will limit you to quests, however the more you do the more you have the choice to unlock other quests. After completing quests, talk to Jeanne (The girl sitting at the radio table). She will bring up a rewards tree. For the first achievement "Beacon of Hope" simply spend all your KW into the only available powerlines to unlock all the shops in Lestallum. It should only take 2-3 quests to get enough KW this early on.
After getting this achievement, many more branches and paths will unlock. The ultimate objective is to fill the tree. Other achievements in this pack are earned as you fill out the tree.
Please note the rewards available before you unlock them as some you may want to prioritize and some you may want to skip. I'd recommend unlocking ones that offer hunting quests as tougher quests offer more EXP and KW, making this grind less tedious.