I extracted this battles/engagements/skirmishes list and casualty information for the regiment in working on the Johnson County book. It is going to end up buried there and I thought I would post it on here if anyone might ever need it.
The sources are the Official Records of the War of the Rebellion, and the individual CSR's--cross-referenced with the Compendium of the War of the Rebellion.

Partial casualty returns, where available, in parenthesis [k.= killed, w. = wounded, c. = captured, w.+c. = wounded and captured. Those mortally wounded are included in the totals for killed (except at Mine Creek where they are listed as mw.). Some battles such as Fayetteville, Pine Bluff, and Marks' Mills are complete returns. Most of the others are incomplete. The Mine Creek returns show only those captured (including wounded and mortally wounded captured) by Federal troops. The other killed and wounded for Mine Creek (in fact the whole Missouri Raid) are not known. Additionally, the Compiled Service Records list 11 others captured at home or while detailed (one of who died as a POW), and 35 who died by disease or accident:

Cane Hill, AR 17 August 1862 (1 c.)
Barry Co., MO 21 August 1862 (1 w., 5 c., 1 died as POW)
Devil’s Backbone, AR 1 September 1862
Boston Mountains, AR 6 September 1862
Sugar Creek, AR 8 September 1862
Keetsville, MO 20 September 1862 (1 w.)
Cassville, MO 21 September 1862 (1 k., 1 c.)
Cassville, MO 1 October 1862 (1 c.)
Barry Co., MO 5 October 1862 (1 c.)
Cane Hill, AR 6 November 1862 (1 w.)
Cane Hill, AR 5 December 1862
Reed’s Mountain, AR 6 December 1862 (1 k.)
Prairie Grove, AR 7 December 1862 (2 k., 2 w., 1 c.)
Huntsville, AR 10 January 1863 (1 k., 1 w.)
Van Buren, AR 10 February 1863 (1 w.)
Hunt, Arkansas 21 March 1863 (1 k.)
White River, AR 22 March 1863 (1 k., 1 w.)
Johnson Co., AR 25 March 1863 (1 k.)
Fayetteville, AR 18 April 1863 (7 k., 12w., 4 w.+c., 1 c.)
Bentonville, AR 22 May 1863 (9 c.)
Boston Mountains, AR 1 July 1863
Cross Hollows, AR 24 July 1863 (1 c.)
Elm Springs, AR 29 July 1863 (2 k., 1 w., 1 c.)
Bentonville, AR 15 August 1863 (4 c.)
Dardanelle, AR 12 September 1863 (3 c.)
Pine Bluff, AR 25 October 1863 (1 k., 5 w., 8 c., 2 died as POW)
unknown, AR 10 December 1863 (1 w.)
Point Remove, AR 15 December 1863 (1 c., died as POW)
Johnson Co., AR 20 January 1864 (1 c.)
Camden Expedition March-May 1864
Spoonville, AR 1 Apr 1864
Antoine Creek, AR 2 Apr 1864
Wolf Creek, AR 2 Apr 1864
Near Prairie D’Ane, AR 8 Apr 1864
Prairie D’Ane, AR 9-12 April 1864
Poison Springs, AR 18 April 1864
Camden, AR 20 Apr 1864
Marks' Mill, AR 25 April 1864 (6 k., 15 w.)
Clarke Co., AR 29 April 1864
Dardanelle, AR 16 May 1864
Pine Bluff, AR 30 July 1864
White Co., Arkansas 15 August 1864 (2 c.)
Price's Missouri Raid September-October 1864
Lewisburg, AR 7 September 1864
Glass Village, AR 8 September 1864
Arcadia, MO 27 September 1864
Pilot Knob, MO 27 September 1864 (unk k. and w., 2 captured)
Franklin, MO 1 October 1864
Moreau Bottom, MO 7 October 1864
California, MO 9 October 1864
Booneville, MO 11-12 October 1864
Lafayette Co., MO 16 October 1864 (1 c.)
Lexington, MO 18 October 1864
Dover, MO 20 October 1864 (1 c.)
Little Blue River, MO 21 October 1864
Independence, MO 22 October 1864
Westport, MO 23 October 1864 (2 c.)
near Mound City, KS 24 October 1864
Mine Creek, KS 25 October 1864 (2 mw. +c., 5 w+c, 40 c, 9 died as POW)
Fayetteville, AR 4 November 1864 (1 c.)