Per Jerry Robinson, he penciled and inked the Batman and Robin figures while Kirby and Simon drew the rest of the cover. Information per Harry Mendryk via the Jack Kirby Museum (http://kirbymuseum.org/blogs/simonandkirby/archives/1465).
Inside front cover. The book "The Lost Caravan" by Waldo Fleming is reviewed.
Trademark information: (Submission) Serial #: 456,728. Detective Comics, Inc., New York, N. Y. Filed Nov. 10, 1942. "The Boy Commandos" (logo image), For Cartoons Published in a Series. Claims use since Mar. 2, 1942. Submission appeared in the Official Gazette of the United States Patent Office, Volume 546, January 12, 1943, p. 220.
The trademark submission was for the logo design that started in this issue. The first appearance in the last issue has a different design. Also, this trademark is not the same trademark that was granted for the logo that would eventually become the cover logo for Boy Commandos (DC, 1942 series) #1 (Winter 1942-1943) (details found on the ashcan, Boy Commandos Comics [ashcan] (DC, 1942 series) #1 (September-October 1942)).
(Granted) Trademark #: 400,764. Registration granted in the Official Gazette for the United States Patent Office Volume 548, March 30, 1943, p. 787.