Please, correct my choices.

[chuhuytam]

Dear teachers.
The army was practicing its drills. One group was doing artillery practice. One group was matching; other one was at attention; and the others was practicing combat tactics.
Please, explain me why they're correct or not. Thanks a lot.

[David L.]

The army was practicing its drills. One group was doing artillery practice, one group was marching, another was at attention, and the others (the rest) were practicing combat tactics.
You are giving a list of activities, so they should be separated by commas.

[Naamplao]

Dear teachers.
The army was practicing its drills. One group was doing artillery practice. One group was marching; other one was at attention; and the others was practicing combat tactics.
Please, explain me why they're correct or not. Thanks a lot.

First of all, you have a very choppy sentence structure. It is a very boring thing to read, the way you have written this. You also use the same words over and over again.

The army was training in groups. While one group stood at attention, others were marching, practicing combat tactics and executing artillery drills.

Can you see how I don't repeat myself? I also combined your choppy sentences into one more interesting version. I purposely chose the group that was standing at attention for the "while" clause as this group was not active compared to the other groups.

[chuhuytam]

Thank you very much.
Both of your reply are really interesting.