Target strength describes the ratio of impinging sound to reflected sound. The target object is placed in the centre of a circle that is X meters radius (typically 1 m), with the speaker facing the object. The impinging sound is quantified by placing the microphone at the centre of the circle (e.g. rms of playback), and the reflected sound is quantified by placing the microphone on the circumference of the circle. It is important to choose the playback sound duration and radius such that the direct path of the playback and reflection are separated in time. Also the walls of the room need to sufficiently far away from the experimental 'circle'.
If the mic and speaker and co-located, then you'll calculate the monostatic target strength. If the speaker and microphone are located at different points on the circle, then you'll calculate the bi-static target strength (See [1]). Remember to ensure the returning echo is recorded with sufficient signal-to-noise ratio - and adjust speaker levels accordingly.
Another experimental consideration is the directionality of your speaker. If it is too directional, it may not ensonify the whole animal. Quantify the beamwidth of your speaker for the playback sound. Also, perform playbacks at increasing distances, and check if the obtained target strength is consistent (remember to also measured received level at the centre for each playback distance!).
And finally, while reporting the target strength - remember to provide the reference distance (-40 dB target strength at 1m). For a more detailed description of a mono and bi-static target strength experiment see [2], which I'm an author on.
References
- Cook JC (1985) Target Strength and Echo Structure. Adaptive Methods in
Underwater Acoustics, ed Urban HG (D. Reidel Publishing Company), pp
155–172
- Supplementary Info Sec. 1.8: Beleyur, T., & Goerlitz, H. R. (2019). Modeling active sensing reveals echo detection even in large groups of bats. Proceedings of the National Academy of Sciences, 116(52), 26662-26668.
Acknowledgement: This answer also owes a lot to a PDF handout (which I can't seem to find anymore online) uploaded by Magnus Wahlberg and discussions with him.