All my bikes run Elixirs, so I’ve had lots of practice. The pro bleed kit really helps, too. Elixirs are a bit harder to bleed than Shimano but not impossible – the key is to have no air anywhere in the system – reservoir or lines – whereas Shimano are happy with a bit of air in the reservoir.
Make sure the pistons are pushed all the way into the caliper before bleeding and insert a bleed block. It’s easier, especially with the rear brake, to bleed if the lever is raised up obove the caliper – easy to do if you have a workstand.
Fill a syringe very slowly from a fresh bottle of DOT5.1 as it froths and gets air in it if you haul on the syringe plunger. Attach this syringe to the caliper bleed point and an empty one to the lever end. Push a good amount of fluid slowly through the system. Remove the lever syringe and junk the old fluid, replacing with about an inch worth of new fluid. Refill the caliper syringe with fluid and reattach. Push a little fluid down from the lever end to push out any air from when you reattached the caliper syringe.
Now, push fluid up slowly from the caliper end towards the lever. Tap the hose as you do this and bubbles will be dislodged. When you get half way through the caliper syringe’s fluid, flip the bars so that the lever is highest, tap the hose, push a little fluid through and then flip the bars down so that the bleed point is uppermost. All the bubbles trapped in there should flow straight out.
After you’ve done this, you should be able to push fluid through from either end push fluid back and forth several times to check) and see no bubbles coming from caliper or lever. Never let a syringe empty, EVER, while you’re doing this.
Finally, remove the lower syringe with the bleed cap ready to screw in. Push a little on the upper syringe before replacing its cap to ensure fluid is coming out instead of air going in as you replace the bleed cap.
I always replace the pads and pump the brakes carefully to push the pads to just above a disc thickness before replacing the wheel. I think you’ll be impressed how good you can get them using this method.