1) Complete Dramatic Log.
2) Unlock New World difficulty in Treasure Log.
3) In the pre-battle screen, go to Results and then go left once.
On this screen, you will see the combined total of all Berries you've obtained through your playtime. This value needs to reach 100,000,000 or more for the trophy to unlock. It will unlock the moment that value is reached from the tally screen in the post-battle results. It does not require you to obtain and hold on to 100,000,000 berries at once, for it would be inconvenient to have to spend money to make money in this game.
In the NW difficulty, most missions can award you anywhere from 1m to 3m per battle on S rank. As an example:
My last mission ever was a random mission I played online that I hadn't got a rank for yet. The final results were:
Clear Bonus: 1,179,000
Earned in Battle: 315,000
Battle Grade S Bonus: 1,179,000
Sub-mission Success Bonus: 235,800
Ally Bonus: 589,500
Coin Selling Bonus: 298,000
Total: 3,796,300
The first category is for clearing the mission, the second is the Berries you obtain in combat from fighting enemies and having it drop, the third is from obtaining an S rank, the fourth is from any side missions that are completed during the main mission, the fifth is from performing a mission online with other players, and the sixth is from selling any coins after you've reached 999 for that specific amount.
I do not know the amount that Cat Burglar may modify this, but this and another skill actually modifies the amount of berries obtained (Cat Burglar is in the result screen, while there's another that increases Berries that drop).