^ The Godzilla game is AWESOME if you want a pitch-perfect video game simulation of what it's like to actually be the monsters as they appear in the movies. It doesn't have any real kind of story mode and the objectives are exactly the same from one level to the next. It's not made for general gamers or anyone who doesn't have a keen interest in Godzilla movies and wouldn't recognize all of the little details that are straight out of the films.
You pick a monster and on each level you have to destroy three big generators, all while absorbing "G-Energy" from everything you destroy and incrementally growing from 50 meters to 100 meters in height. Most levels have at least one other kaiju that eventually shows up which you must defeat in order to proceed. As you destroy buildings and military forces the disaster level builds on a scale from 1 to 5 as you proceed through the story mode. At each disaster level the G-Force weaponry that you face gets upgraded, from helicopters and tanks to full-metal missiles, maser tanks, maser jets, cadmium missiles, all three versions of the Super-X, the 2004 Gotengo, and the 1993 and 2003 versions of Mechagodzilla. This is the "invade" version of the story mode and you can play it as four different versions of Godzilla (1964, 1989, 1995, 2014), Anguirus (1968), Rodan (1956), King Ghidorah (1991), Gigan (2004), Battra (larva & adult), Spacegodzilla, Hedorah (4th form), Biollante (2nd form), Destroyer (4th form), and Mechagodzilla (1974 & 1975).
You can also play the "defend" version of story mode in which your goal on each level is to defeat the invading kaiju before they destroy 50% of the city or two of the three generators. You can play this version of story mode as Mothra (1992, larva & adult), Jet Jaguar, Mecha King Ghidorah, and Mechagodzilla (1993 & 2003).
There really isn't more variation to the gameplay than that, and there are only about 10 different stages so some of them do repeat even on one playthrough of the story mode. Like I said, it's not really a good video game in a vacuum, but if you're a Godzilla fan who just wants to play as the monsters from the movies and you'll appreciate the accurate design details and all of the little character attributes and sound effects from the films, you'll really like playing the PS4 game whenever you feel like it. It blows all of the Atari/Pipeworks Godzilla games out of the water.
Unfortunately it seems that Bandai's license for the PS4 game has expired and it's now out of print. The cheapest used copy on Amazon is currently $43 and new copies are listed for $73. I think it was removed from the available downloads on the PlayStation Store too. If you have a chance to get it for cheap then definitely snatch it up. I know there was a lot of backlash when the game came out in 2015 and a lot of gamers sampled it and ended up selling it quickly, and I've seen a lot of used copies for cheap prices at GameStop stores in the past few years.