A way to do it that might not generate such a large trace file :

1) find the users's session in V$SESSION, get the SID and serial#

2) execute the following :
exec dbms_system.set_sql_trace_in_session(sid, serial#, TRUE);

3) to stop tracing - its the same command except with FALSE as the 3rd parameter.

no matter which way you trace, you might want to set the MAX_DUMP_FILE_SIZE parameter. This parameter determines how big the dump file is allowed to grow...