I only got the game yesterday and I no I'm a noob but on the mision were..

It might be a bit hard sometimes but i'd say just go for it and try and kill the wyvern! That way he dosent get in the way and you get more expensive items. If that dosent work try and find the carry skill on the internet, you need certain types of amour which then makes you able to run with eggs and rocks almost as fast as normal!

What I did was just wait for the wyvern to fly off to another area. To kill some time just defeat the velociprey on the other areas so hopefully when you cross back to your tent they'll be out of your way from being attack and from dropping the egg. Hope this works. Also, don't forget to increase your stamina to full bar.

Before carry the egg, full up your stamina bar and then take the power juice. The stamina bar turn to white color. Keep on running the stamina bar won't drop for a long period. Some mission need you take three eggs, so make 3 power juice. The power juice is the combination of Catalyst and Rear Steak. How to get the Catalyst? Catalyst is a combination of Honey and Bitterbuy. Try it!

The way I did it is not to kill the Rathalos, but to sneek past it
The first thing you do is go to the BLUE Chest and pick up all Ratchons and potions or first-aid go to the sector with all the velociprey and one wasp. Kill all of the velociprey and go to the place where you first see the rathalos hide until it flighs away
Go up the two ledges and go inside the large hole in the wall
In there you will find about four velociprey, kill them
Go up the ledge and you will see the nest,
Eat and drink all rachons and potions
Then pick up the egg
Head back to camp
You can run, but don't let you stamina run out or else you will drop the egg
WATCH YOUR STEP! Don't jump off of high ledges