New Edit 12 Oct 2018
It appears that this achievement is actually possible by repeating the same table over and over. So in theory anyone can get it with enough time and patience. Thanks to multiple TA-ers for clarifying in the comments.
I will leave the old solution below for tips on high scoring tables.
As of the new patch (13 Dec 2017) this achievement now requires you to score 1,000,000,000 points over MULTIPLE tables. These scores will need to be new scores (ie after the patch) to count towards the achievement [thanks to silent 3rd and Exe the Hero for clarifying].
I will leave the old solution below for reference (or if you want a quick method to get the points) but obviously this is now far easier. Thanks to MistaCelestial for confirmation of the change.
The following tables are recommended high scoring ones.
Marvel: Women Of Power - This should be your first stop for a big scoring table. Even without any kind of guide it's very generous indeed, but a helpful tip is to try for the Squirrel Girl Multiball as often as possible. A more thorough walkthrough is contained in the old solution below.
Sorcerer's Lair - The free table is an excellent source of points. If you can make it through to the wizard mode by attempting (you don't have to complete them) each table challenge, you'll be looking at a big score, as the final mode is very generous with points.
Epic Quest (recommended by x Mataeus x) - His full guide can be found in the comments, but suffice to say that this table tracks your level over multiple games, so after a few plays you'll be getting much bigger scores.
Feel free to add your recommendations in the comments and I'll update the solution! :-)
This achievement requires you to score over a billion points (1,000,000,000) on a single table in one attempt (three balls).
It's possible on any table, but you can make this achievement slightly easier by choosing the Champions table, which is part of the Marvel: Women Of Power pack. This is a very forgiving table, but more importantly a high scoring one.
The table guide (credit to ShoryukenToTheChin) can be found here.https://blog.zenstudios.com/press/assets/table_guides/C....pdf
The trick to big high scores on this table is to boost your multiball power-up as much as possible. Then you'll be trying to perform the Squirrel Girl Multiball as often as you can. This is a big scoring mode where you'll be aiming to hit Jackpot ramps as quickly as you can. Once you hit one you'll get a short window to hit another for a Super Jackpot, and then another short window for a Double Super Jackpot. With your multiball special maxed out, you're looking at around 60 million points for a Double Super Jackpot, and you can get plenty of these per multiball activation.
Video of how to unlock the multiball mode:
Video showing multiball scoring:
If you accidentally start a different mode don't worry, it's all very generous and high scoring so you should hit 1BN without too much difficulty if you're half decent at pinball.
For those people who haven't bought any tables, it is possible (albeit far more difficult) to do this on the free table, Sorcerers Lair. I recommend using the combo time extending power-up, maxed out as much as possible. This makes performing combos more forgiving, and if you can pull off a 6-way combo you'll light the Extra Ball ramp at the top left of the table. Do this first on every ball and you should extend your game pretty significantly, although you'll probably be looking at three or four times through Wizard mode to get to a billion.