This Solution takes into account the glitch which means that possessing a dog = death. Thus, the dog must now be last.
Set Up: You will need a minimum of 13 runes for ALL the possession upgrades by Mission 5. There are plenty more than this, so don't worry if you miss a couple.The above amendments are very good, so credit to them and in particular Late Night Gamer on youtube (well done, sir.) However I would suggest making a slight alteration which makes it SIGNIFICANTLY easier, in my opinion.
Many Solutions have the order - Rat >
Fish > Human > Bloodfly > Dog (who dies)
My solution switches the human and fish - Rat >
Human >Fish > Bloodfly > Dog.
The reason for this change is that timing is EXTREMELY TIGHT. The fish is the hardest to move, and this method means you can look to your right and just spam RT until it instead of trying to chain to a human with a patrol pattern that means he's not always visible.
Go to Mission 5. Go through the mission stealthily until you get to the conservatory, and disable past the wall of light by the watchtower. In laymans terms, follow Late Night Gamer's video p until 2:25 (ish).
u Watch the whole thing once, regardless, as the video does the correct route, just in my opinion not the easiest order (not a criticism, as I said he did a great job).
After opening both doors in the video make a manual save (around 2:25 in the vid). Possess the rat (1) with LT, as the video shows. However, instead of possessing the fish, chain possess the human (2) straight ahead with RT. This will make things easier, as possessing the human as a fish is very tricky. As the human, look into the pond and chain possess the fish with RT (3). As the fish, it should be much easier to look to the right of the pool and spam RT to chain to the bloodfly, instead of trying to peak above water and get the human. As the fish, chain to the bloodfly (4) and fly through the gate shown in the video to the dog (5). You will die, but the achievement should pop regardless.
If it doesn't work, just reload save.
Summary of route.
Posess Rat (1). Run under tunnel and possess human (2). As human, possess fish (3). As fish, look to right of pool as you entered through tunnel and possess bloodfly (4). As bloodfly, fly across and through the gate, and possess dog (5). Achievement should pop.
*notes - unconscious human are possessable. which theoretically would eliminate the problem of the patrolling guard. However, with bloodflies around the human will quickly be killed if unconscious, and no longer possessable, so I do not recommend leaving an unconscious guard by the pool.*