I've been a professional long-lens bird/nature shooter since the 80's. I used to use very big and pricey dedicated video cameras/lenses, but now have found the wonderful micro-4/3 world and love it. I've gotten some amazing shots, both video and stills, by adapting older long telephoto lenses to my Panasonic G6 and GH3, as well as my Olympus E-PL5 and E-M5 Mark II.
For convenience and smallish carry-along lens, the Panasonic Lumix 100-300mm does a good to very-good job as long as you learn how to use it and shoot with good technique, but for my super long tele shots, I found a Canon FD 500mm f4.5 lens (built in 1989 - big and in pristine condition, it's very good glass and cost $1300) which adapts very easily to micro 4/3 cameras, but requires you to focus manually and learn to use the focus assist built into the cameras.
If you are serious about getting great telephoto shots, there are lots of Canon, Nikon and other telephoto lenses which can be adapted for manual use on these small micro 4/3 wonder-cameras. Keep in mind, none of these options, including the Panasonic 100-300, is going to give you high percentage focus accuracy for moving bird/critter for stills, but will, with practice, allow good focus when shooting video. You have to have a camera with a good viewfinder or a focus device on the rear LCD, regardless.
Olympus is supposed to be releasing a 300mm f4 in the early part of 2016 which should focus faster than any other super-telephoto now available and be very sharp, too. Supposedly Panasonic will be offering a 100-400mm in 2016, as well, which is said to be a better lens than the 100-300 now available.