Listed below are the various ways you can get Diamonds, four of the five ways are will enable you to get them for free.
Real Money
you can spend real money at the in-game store.
Watch Videos
An easy way to get Diamonds is to watch the advertisement videos where you can earn 3 diamonds a day. This can give you 90 Diamonds a month if you do this daily for 30 days.
Play Solo Events
you can earn Diamonds by reaching a certain rank in an event. for example you can get 70 Diamonds for coming int the Top 230 in the Savvy Shipment Event.
Complete missions
When you complete chapters you will be rewarded between 10-15 Diamonds which will quickly add up into hundreds of Diamonds if you complete the entire mission.
Gang Battles
Playing as part of a gang in Gang Battles can be lucrative. for example if you join an active gang which comes in the top 500 you will be rewarded with 100 Diamonds.