You start the game with your monsters at the bottom of the screen. After the game starts, it is time for you to start the 'urban renewal' process.
After you start, you will start being attacked. There is no real way to avoid a lot of the attacks by the National Guardsmen due to the sheer volume of fire they are laying down. Your best bet is to keep moving and make yourself a hard target to hit.
To move quickly from building to building, jump toward the building and push up to grab the building. This enables you to use your monster's ability to both jump and climb at the same time.
To relieve some pressure from the National Guardsmen, climb up the buildings and smash the windows where they pop out from or just eat them when they are leaning out the window. Move quickly since their buddies are still shooting or throwing dynamite at your monster.
Unless you are totally obsessed with points, let the National Guardsmen do your work for you. A great example of this is that about midway through a day, a National Guard-man will rush out from the side of the screen with explosives. They will place them at the base of a building. This demolishes the building and helps you along to the next day.
Another way to destroy buildings is to weaken it up, then jump on the roof. Your monster's weight will cause the building to collapse.
The air units can be rather dangerous. During the beginning days, the helicopters will overfly your monster, turn around, and then dive in for the attack. You can destroy the helicopters when they are coming in to prevent their attack. Also, when you are moving around, you make it harder for them to get a bead on your monster.
During the later days, helicopters will drop bombs. Again, paying attention to everything that is going on will allow you to easily escape the bomb being dropped. You can also entice the helicopter to drop a bomb when you are on top of a building. When the bomb is dropped, jump out of the way and let the bomb do the damage to the building for you.
Make sure that you either grab the food or eat the National Guardsmen to keep your health up. If you can hold out for 128 days, you will get all of your health restored for that day and days 256, 384, 512, 640, and 768. Also keep in mind that if you punch too fast, you may end up getting something that will harm your monster.
Paratroopers can be a particular pain. If you plan to attack a building with a Paratrooper unit on it, make sure you quickly scale the building and eat said unit. It makes life a lot easier since their rapid fire can put a major hurting on your monster.
Ground units such as Tanks and Police Cars can be a real nuisance. They fire some pretty heavy shells which not only cause a lot of damage, but they also can knock back your monster for quite a distance. There are some ways to combat these units :
1) Climb quickly up a building. When the unit passes below you, jump down and give it a good punch.
2) Time the shots and rush the ground unit in-between shots to get a good punch in.
3) Use available weapons such as manhole covers, flower pots, or safes to drop on them. These things also allow you to hit them at a distance.
Be sure and watch what your monster grabs at. There are a lot of hazards in the buildings and it is pretty bad when your monster buys the farm doing dumb stuff such as grabbing electrical items such as toasters and light bulbs.
In addition to the above, dynamite is sometimes in the middle of buildings. When uncovered, you have about two to three seconds to get your monster out of there before they are blown off the building. Eating it will only decrease your monster's health so run far away when it is uncovered.