It really depends on the type of triathlon. Training for a sprint triathlon is much different than training for an Ironman. Depending on the distance of the triathlon, the athlete may spend most of their time on endurance for running, biking and swimming. Many triathletes do not come from swim backgrounds and need a good swim instructor to master this. It really depends on the athlete and the type of triathlon.
Fitness and Nutrition Coach
In addition to the good advice above, the training plan can also be affected by where the triathlete is in their season (off-season, start, mid, etc) and how competitive they are.
If you listen to Frazier Quelch, former triathlete and head of training and development for TRX, the most messed up his body was was when he was a competitive triathlete. While a serious athlete might be willing to sacrifice their body for sports excellence, others may not. Hence my comment on how competitive they are and whether they are.
The only two triathletes I’ve worked with (one had done 6 iron mans and her husband had done one) I worked with them off-season. I put them in the frontal and transverse planes to support the directions that were less efficient.
To strengthen your core, try a Superman plank. http://www.plankpose.com/core-killer-superman-plank/
It’s a great exercise for advanced users