If you are looking for as near to impossible nut locking short of wiring (not recommended for parrots) target Birdman666 recommendation.
Locktite is now available for very wide number of applications. The most common problem with Locktite is the general human belief that if a little works well and lot will work even better. Which of course is not true with most things mechanical, electrical, etc, etc...
The two types that you most likely would be looking at is Blue or Red. Over use (placing far more than recommended and/or needed) will cause either to in fact reduce their locking abilities and make the job look like it was done by a, well you fill this part in.
Blue is used for industrial applications along with a torque specification. Proper torque practice required. The 'very thin' layer of Blue Locktite improves the shock holding capacity of the torque specification. The nut can be removed, but may require up to twice the original torque specification. General Application Use.
Red is also used for industrial applications along with a torque specification. And again, proper torque practice is required. The 'very thin' layer of Red Locktite also improves the shock holding capacity of the torque specification. The nut can be removed, but commonly requires heat to cause the Red Locktite to release. High Shock Applications.
Locktite is available for Aircraft applications, but its applications are very specific as is the color. It is rare to find this type of Locktite outside of its industry.
The use of more than a 'very thin' layer of either Locktites will in fact greatly reduce their holding abilities and is the most common reason Locktile fails to hold. The sad reality is that the nut would have greater torque holding abilities if Locktite was not over used to begin with. Point being, use to much and the nut will release a much lower torque levels.