If you add friends in Bleach: Immortal Soul you will be able to send each other hearts which can then be redeemed in the shop for various useful items. Tap the 'Friends' option in the upper-left corner of the main interface to add friends.
Check Out the Shop
Make sure you regularly visit the shop and check out the item deals. Each day there will be different items on offer there that you can buy using the Gold you have earned. These items include Character Shards and Soul Stones.
Complete your list of daily tasks in order to get rewards which will help you improve your heroes. Furthermore, for each Daily Quest that you complete, you will also obtain Activity Points that you can trade for more rewards.
Focus on Story Mode
When you begin playing Bleach: Immortal Soul focus on trying to advance as much as possible in Story Mode by completing as many of the stages as you can. Do not worry about completing them with 3 stars at this point as you can always return to re-play a stage at a later time. If you do this you will be able to unlock Chad, Rukia, Uryu Ishida, and 2 more forms of Ichigo. These characters are good enough to use until you get the opportunity to unlock some stronger ones.
Free Soul Jade Summon
Each day you log in to Bleach: Immortal Soul you will have a free Soul Jade Summon which will enable if you are lucky to pull some powerful SSR heroes which will help you progression in the game significantly.
Get 3 Stars
It's worthwhile trying to clear a stage with 3 stars as doing so will enable you to sweep it the next time and get instant rewards. Getting 3 stars in a stage is one of the best ways to grind materials, EXP tonic, and EXP in Bleach: Immortal Soul.
Join An Active Squad
If you are an active player you may want to consider joining a Squad. Being a member of a squad allows you to donate Gold to earn Prestige Points which you can then use in the Squad Shop for War Soul and Soul Stones, which can then be used for Charcter Enhancement.
Don't forget the Milestones quests as these allow you to earn Omni Shards which can be used for SSR and even UR characters to unlock completely.
Missions and Events
Character Shards can by obtained from completing missions and participating in events when they become available so consider these options so you give yourself the opportunity to unlock stronger heroes by having the required number of Characters Shards.