Looking at your in-game map, you will notice hollowed out star icons. These star icons signify training challenges that you can complete for massive PP bonuses, making these important for both leveling progress and for the achievements. All of the challenges task you with killing a certain number of enemies with a certain type of weapon or vehicle, such as fire or electric weapons, combo weapons only, or unarmed only within one minute. Many of the challenges can be completed using the Rollerhawg to quickly roll around the nearby area killing enemies, and the more difficult unarmed ones can be completed using the unarmed bonus damage book and the knee drop combo.
Some quick notes: fire weapons can include the Rollerhawg, Flame Mecha Dragon, Flame Arrows, etc. and does not include explosives. Electric weapons can include the Elecrtic staff, Rolling Thunder, and shockdozer.
Also note that you can go anywhere during the challenge, and you're not confined to a particular area, however you will want to plan out where you go prior to starting the challenge to maximize your kill efficiency.
You can check out THIS playlist for a few videos that give you the general run through of the different types of Survival Training missions.