Okay so I'm pretty sure I found the main issue here.
The only attack animation you had in the animations tab was SwingClaws01 while there is supposed to be 2 more: SwingClaws02 and SwingLaunch. The enigine probably saw that you didn't have those so the monster would instead do nothing and would only attack you when the engine would decide to play the SwingClaws01 animation. So just add those 2 (you can use the same animation for SwingClaws02 as in SwingClaws01 btw) and it should fix the problem
About the animations, for your first animations they were ok, mine actually looked excatly the same when I started animating xD The biggest tip I can give you is to import the grunt's animations in maya and frame by frame look at the movement in the arms, legs, hips, torso, especially the hips and that will help you alot to improve your own animations. You can also use IK handles and other controllers for your rig (basically tools that make animating alot easier and better), just look those up on youtube and it should be fairly easy to make them for your rig^^
Don't stop animating and make more monsters to animate for your project to help you improve in both modeling and animating! The more you do, the better you become, trust me, it took me alot of attempts to make animations for my first monsters look good. I mean dear god, look at these first animations I did for my first monster(that also looked like shit) a year ago:
https://www.youtube.com/watch?v=t5iLDwlyMLM and look at how I improved over about 8 months and re-made both the monster and the animations:
https://www.youtube.com/watch?v=nG2gk1jZgjY And I'm still improving and learning new things and techniques!
Anyway, hope I helped you and let me know if you encounter any more problems!