For first badge, fire+water= Energy, water + earth = swamp, swamp + energy = life, earth + fire = lava, lava + water = stone, stone + life = golem, water + life = Weeds.
HOW TO GET HARD BADGE:
1. Have all of your troops in 1 army and drive down into the ukraine and eventually into china. Once you reach the fork in indonesia, send out 2 armies, if you dont take both at once, or if enemey manages to get into india, then restart.
2. Just start yourself in australia or south america and focus on taking whole regions over just mass territory.
3. This one is the hardest. I prefer to start in the eastern asian regions (i.e east china, india or indonesia) then focus on taking sections. You might want to drive some armies into oponents land to prevent them from getting extra troops, though try to focus on not having your borders penetrated, because then its a cluster.
4. Drive your way through spain/france while using your first couple airdrops to give your teamate reinforcements. Try to confront the enemy large armies with your larger armies before they can take your surrounding less defended regions.