A manga about the adventure of a pair of brother and sister in a game world
I believe you are looking for .hack//Legend of the Twilight.


It's about a game called The World.
People can freely log out, including the main characters.
The main characters are a boy named Shugo and his twin sister Rena.
Rena's outfit is quite revealing.
There are hippo-like creatures, called Piikey. Hotaru, one of the female side characters, has one as a pet. Komiyan the Third, one of the male side character, uses one as a mount. Both main characters find Komiyan annoying.
The Phoenix Down (aka Phoenix Feather) is used to save the life of Hotaru's Piikey.
One of the GMs (Game Masters) loves to organize events. One of those, I faintly remember being a race involving swimming.