Honestly, you might just need to wait and acquire more rares/epics to upgrade and reborn them. For some units (Naga, Untouchable) get really powerful once you reborn them. And like what the other poster said, joining a guild is great to use some boosters to increase your units atk/hp temporary. They last relatively long and is a good way to patch up some weakness, such as one shot potential.
Also, might I ask what units are you currently using in your team? You also said you got a few epics. Some are good, but others can easily help propel you a league or 2 higher than you would otherwise without it. I myself was stuck on league 20 for a day or two until I finally found a void juggler to help with damage.