A step up from the Haunted Museum franchise, and honestly a step up from the Tomb Raider franchise, is the Lost Land Adventure game. 5 levels of rough and tumble treasure hunting, idol snatching, gold grabbing, and monster shooting. Had the mouse disappear in Stage 2 boss for a few seconds, and for some reason couldnt find a way to quickly select the final level (had to wait for it to count down) so a sub 40 should be easily possible.

Start (First Level Appears) - 00:27

End (Final Hit) - 41:22

Total - 40:55