Grats on getting to the next tier!
Again, when it comes to most 4-stars, Chains are super helpful, but not mandatory. With the right combination of buffs, you can hit those cap-breaking numbers on an Awakening, easy. And hey, three Awakenings is nothing to sneeze at.
But yeah. Much like with 3-stars, with 4-stars, just work your way around the circle. Start with the ones you can beat consistently, improve your deck, replace 3-star with 4-star options, and move from one to the next. Thankfully, they've improved 4-stars so that instead of random chance drops, you get one of each - that will let you level them up pretty quickly once you can consistently beat them.
4-stars are also a great opportunity to Inherit on those freebie 5-stars. I particularly like Kraken for that, since the Magicite you can get include Blade Ward and Spell Ward, two skills that are pretty helpful in any given deck. (Put both on a Madeen and just use it all the time!)