You can get both sticky and regular grenade kills towards the end of the level Ghosts when there are 3 separate groups of rats in two adjacent rooms with 5-6 rats in each group. You will need to run ahead of Khan to prime and throw the grenades before he activates the respective groups' movements (their locations are very obvious). The checkpoint is also right before this section.
It should be noted that I did not receive the "Ka-Boom!" achievement at the same time as the "Sticks like a bur" achievement, though a quick checkpoint reload solved that problem.
Credit for this solution goes to O918 on XBA.