[Dan Hibiki]

Use a fast fighter instead. Dhalsim is slow as ####, and would get stomped by God Rugal. I suggest Ken, Ryu, Gouki, Dark Ryu, or Nakoruru. Don't use Shin Gouki against him unless you are really good with him (Shin Gouki takes serious damage).

If using Dark Ryu, Gouki, or Shin Gouki, counter-teleport when God Rugal teleports. Roll (or dodge) when God Rugal uses the Shun Goku Satsu or his dashing-slam-you-into-the-wall super (I made up that name myself). For Gouki/Shin Gouki, use the aerial fireballs each time you jump (forwards or backwards). The best super move for each character against God Rugal is:

Ken: Shoryu Reppa
Ryu: Metsu Shoryuken (?)
Dark Ryu: Shinkuu (?) Tatsunamisenpuukyakuu
Gouki: Messatsu Go Shoryu
Shin Gouki: That drop down from above thing
Nakoruru: That hawk attack thing where it dives at him

Basically, quick is the key, and Dhalsim doesn't cut it.