How to ship a LEGO sculpture to a contest?
As @Mołot commented, first ask the contest committee whether they have specific rules. In general though, shipping in chunks is common, ideally few pieces that are simple and straightforward to attach.

Rigid, sturdy builds are obviously going to stand up better to the travails of shipping, so try to avoid spindly construction. Follow good mechanical engineering principles, and if you can use technics for internal support, it may be very useful.

Glue also helps - yes, it's a bit more permanent, but for this type of production, you want that.

Additionally, shipping with "popcorn" pieces densely packed really helps prevent damage. Be aware that whoever unpacks it may be less keen :-)