* Craft a bunch of the blue enchancement core tonics and use them at all times. * Run echoes battlegrounds and use the hammer on pistons and collect radiolite and kill the demolisher every run too, then turn in your radiolite when you run out of charges or are full on radiolite as it will give you tons of rep for Failsafe and cores and items to delete. (can go do the beacon afterwards as well) * Claim blue armor from collections and upgrade until you spend 1 prism then delete the armor to double your cores from the 3 you spent on the armor to 6 cores you can do this as long as you have prisms. * Claim the echoes quest item so you passively get echoes engrams to claim and delete for potential cores. Those are some quick ideas to increase your core count.