If you are playing the tables themselves and not doing the Bloody Challenges, this is a fairly easy achievement to unlock, unless you're pretty terrible at pinball. Admittedly, Zombie Pinball's tables are poorly designed, with many of the ramps pointed at the ball drain between your flippers so that if your ball does not actually go all the way up the ramp, it has a fair chance of draining out. To combat this, you can use the table's Tilt function by hitting Y as the ball comes down the middle of the table. This should shove the ball to one side or the other, saving it from draining. Once you get the hang of this, you can play a table basically indefinitely, especially if you're good at keeping balls going after activating a multiball mode.
Earning 100 million points is pretty straightforward, all you need to do is just keep bouncing the ball around and completing modes. You'll have 5 balls to start with, and it's possible to earn an extra ball during play. Activate multiball modes as often as possible, and keep them all bouncing. You earn more points during multiball modes.
The biggest thing you can do to increase your point gain is to increase your points multiplier. To do this, you need to activate all of the multiplier insert lights, located usually on the right side of the table, often above a bumper (or set of bumpers). You'll see downward pointing arrows pointing at the lights in question. One of the arrows will be lit at all times; it will slowly rotate which one is lit every few seconds. The arrow that is lit is indicating which path the ball is going to take when you send it up the ramp that leads to those lights. You can change which lights are active or not by clicking the flippers, which rotates the lights in a set order. Lighting all of these lights turns on x2 multiplier and turns off the lights; do this over and over to increase the multiplier all the way up to x8.
It is important to note that the multipliers RESET every time you complete FINAL MODE. So if you manage to complete all the required modes and finish FINAL mode before hitting 100mil (which is pretty likely), you'll need to build up your multiplier again.
Please note: the achievement will not pop when you hit 100 million points, but rather when you end the game with more than 100 million points. So if you're just going for this, once you get to 100 mil, just let the ball drain until you're out of balls and the game ends.