Why are you so keen to get her to use tampons? It's her choice to use tampons or not, and if she is not comfortable with using tampons then just let her get on with it. Even if she was okay with using internal sanitary protection it's best to use cups rather than tampons as they're safer, cleaner, more convenient and more reliable.
Tampons are strongly linked with TSS, commonly cause vaginal infections and increased menstrual cramps, and may pose long-term risk due to toxins within many brands. Younger women are at higher risk due to delicate vaginal tissues and not-as-strong immune system - delicate vaginal tissues would also mean they're more likely to irritate or cause pain on insertion too.
Tampons are also far from convenient - they have to be changed every 4-6 hours, cannot be worn with very light flow, overnight, before periods or if she has an infection - tampons also leak, and for swimming there is the issue of the string being on show.
Menstrual cups have NO HEALTH RISKS at all, they can thus be worn for 12 hours, with any flow, overnight, before her period and while swimming with nothing showing outside her body. These are much more convenient and reliable than tampons so a better option.
If you are determined she uses tampons then it depends on what it is that worries her about using tampons. If it's down to ease of use then go for non-applicator as they're less complicated, give more control over depth/direction and have rounder tips. Go for lightest absorbency, and cotton brands like Cottons or Natracare - cotton is softer than rayon as used in brands like Tampax and Lillets so not as rough or irritating during insertion, also less risk of TSS and infections, plus these don't contain toxins.
Obviously if she uses tampons make sure she knows the risks and precautions, and at least make sure she's aware of other options like menstrual cups, softcups, diaphragms, sponges, wet tampons, etc. that all can be worn during swimming too.