@jendeeb
Garden Warfare 2 has what can be considered an "online" and and "offline" mode but both require the PS4 to be connected to the Internet. The game stores all of it's information on the EA servers so it needs to be able to talk with them, so an Internet connection is required.
As to playing the actual game; in order to access true online Multiplayer and Co-Op you'll need to have a Playstation plus subscription; that's pretty much standard for any game which wants to connect with other players.
Luckily the game features an "offline" mode which allows you to play either by yourself or Split Screen with someone on the same PS4 so you only need to be connected to the Internet so the game can talk with the EA servers. You'll find that what serves as the Multiplayer portal in the Plant and Zombie bases will offer you the chance to have 12v12 battles with AI, or computer controlled, opponents and teammates so you can still get the rough equivalent of a big Multiplayer battle. The AI isn't as skilled as other actual players would be but it's good enough to have some challenging fun.
Each base will also feature an area which will give you "offline" Co-Op play as well; when playing alone you'll be able to choose up to 3 AI teammates who you can switch between and if you play Split Screen you'll be limited to a team of just you two but it's otherwise identical to what you'd experience with human teammates.
When you unlock Infinity Time that play mode will be unchanged except for the fact that other players can't join you to form up to a team of four.
The only part you'll be locked out of will be the Mystery Portal which opens for four days 3 times a month inside of Town Hall. The Mystery Portal offers special game modes, a "Super Mix" event which is regular Multiplayer with crazy rules or conditions added, a "Cats vs Dinos" mode which features the Giant Robots from Infinity Time and a "Boss Hunt" which is a super tough cooperative play mode. All of those games require Multiplayer access so without a Plus subscription you'll be denied access I believe. The offshoot from this will be that you'll have a tough time earning Rainbow Stars and those special Stars are used to unlock the Trials of Gnomus and certain special character classes and customization items but none of that is required to simply enjoy the game.