You can 1 cycle this phase and skip the bomb fish coming out simply by quickspinning or jump attacking the eyeball. After hitting him take Iron Boots off.
It it possible to regrab morpheel after hitting her four times instantly.. To do this you need to get on her back with the Iron boots on, this is so when you force un-equip the Iron boots (by equiping an item over them) you will instantly fall off her without waiting for her to shake you off. You can then clawshot instantly to get back on, or equip boots and clawshot to get back on, although putting the boots on again is harder. It may seem like regrabs don't work randomly but there are a few factors to take into consideration when going for regrabs which can make the difference between getting the regrab and missing it.
Zoom out the camera and make sure morpheel is heading down, or horizontal. If she is going upwards it will fail, if she is going horizontal it is more likely but would be slow, if she is going down you will get the regrab and it should be quick
Make sure morpheel isn't about to turn a sharp corner when you force unequip Iron boots because she will get away from you and you won't get the regrab
Don't attempt a regrab if pillar parts are falling around you, however it is rare you will be in this situation
She shakes her head 3 times before she throws you off.