Your first opportunity to get this will be on the second mission. As you progress make sure you search and collect items from anything with a glowing green light as that will usually have items that can be useful for crafting later on.
In the room where you restore the power and the people run through after power is restored, there will be a room that requires a pass code (from archive log at access terminal near save point; pass code - 0340). In the locked room (enter pass code to enter) there will be med-kit blueprints to collect as well as other items in here.
To craft the med-kit just hold down the B button then select the med-kit blueprints. Select the parts required to construct it, press LB to then craft the med-kit. Once this is done you'll have the achievement.