Stay close and keep feeding the basilosaurus. Straying to far can reset the taming meter. If the taming meter resets your taming effectiveness leaves off where you left off. If this happens your best to kill it and try with a new basilosaurus.
This creature is so easy to tame. All you need is:
1. An Ichthyosaurus(these guy won't be attack by any water creature, except the jellyfish)
2. Anykind of meat(I suggest using prime meat and don't use fish meat)
3. Find one of these creature
4. Feed it prime meat(It's a long time between the 1st and the 2nd feed, after the 2nd feed it's fast)
And then you get one of these, just be careful of the megalodons, they will attack right after it is tamed. I hope this is useful for you<3