Yes, when you go to the Almanac, go to Stats and scroll down. You can click Copy Achievements, it'll copy it to your keyboard on your computer or phone, then post them somewhere (I use Discord), go on the relevant device, highlight it, click Copy, and in the same section of Stats, click Load Achievements.
There's also a mode you unlock once you get enough Achievements that lets you do the same thing, but for individual runs instead. So you could start a run on one device, and finish it on the other.