I am trying to fill the I131 form
In "class of admission" field what needs to be entered ?
on my passport last entry at airport say "ARC" is that it.
Judging by your signature, you're an LPR, so your class of admission is "LPR". ARC stands for "Alien Registration Card"
also what is the criteria to "expedite request" ?
USCIS has some criteria under "Tips for Filing Petitions and Applications to the NBC":
under I-131:
.......
Expedite Requests
1. If an applicant has an urgent need to travel and has already filed an I-131 with the NBC, the applicant or his or her representative should visit the local Field Office by making an InfoPass appointment or call the National Customer Service Center (NCSC) at 1-800-375-5283. The Field Office will consider the merits of the request, and will forward requests that they determine to require expedited handling to designated points of contact at the NBC.
2. If an applicant has not yet filed an I-131 and needs an expedited Advance Parole document, the I-131 may be filed in person at the local Field Office after an InfoPass appointment has been made. IMPORTANT: Note that expedited processing is done at the discretion of the Field Office, based upon the evidence provided by the applicant.
3. If an applicant has an urgent need to have a I-765 application processed to receive an employment authorization document, the applicant must make an InfoPass appointment and visit the local Field Office. The Field Office will determine if the applicant’s situation warrants expedited processing, and, if so, will forward the request to designated NBC points of contact to process and expedite the case.
4. Please keep in mind that expedite requests for applications and petitions will be considered based upon the following criteria:
Severe financial loss to company or individual
Situations of extreme emergency
Humanitarian situation
Nonprofit status of requesting organization advocating the cultural and social interest of the United States
Department of Defense or National Interest Situation (Note: Request must come from an official U.S. Government entity, stating that delay will be detrimental to the U.S. Government.)
USCIS error
Of compelling interest to USCIS