Training mode was my friend for learning a 7 hit combo. You can't earn this achievement in training though, you can either do it in arcade mode, or the much friendlier "Local Match" multiplayer. I used Chun-Li in classic mode to get thisy.
Perform the following combo against Zangief to get the achievement.
1. Fill your meter.
2. Use your super. Hold for 2 seconds then , , Any kick (6/7 hits.)
3. Follow the super with Chun-Li's Upkicks. (8/7 hits.)
To perform the Upkicks, hold down for about two seconds, then press Up and any kick button. Make sure you charge the down direction while she is performing her super move.
Practice, Practice, Practice. You need to LEARN good execution, you can't just use it. Chun's timing is very lenient though.
You should do it in classic mode, Local multiplayer. Either should work.