I wanted to add my findings having recently gotten this achievement. The reason I wanted to add this guide was to help with the two main tricks (or glitches) in the game while they're fresh in my head. I had trouble with these at first but after a decent bit of practice i was able to pull them off fairly regularly but found little in the way of in-depth explanation.
An important note which i mention below that needs emphasising - pausing the game does not pause the timer. If you need to look things up, save and quit to the title screen then reload your save once ready.
Firstly, watch this video, its by RiskyCB who holds the current world record. In this video he explains everything that's going on which is immensly helpful:
This is a link to RiskyCB's channel as props:
https://www.youtube.com/channel/UCTifUSFYQxe8TdHNzYgx3jAThe tricks:
Small MechRiskyCB explains it in his video but to clarify - you need to press eject (

) on the frame that the mech appears after saving. I did it this way:
Stand in the save point.
Press eject and Kiki will stand on the gun of the mech.
Press jump (

) so she lands on the save point floor and you kind of get sucked in to the middle and the game starts to save again. HERE IS WHERE YOU NEED TO BE READY TO PRESS EJECT (

).
The tube comes down from the top, encases the save point at the bottom and retracts back up. You need to hit the

after the full traction of the tube but before the full screen flash. This is a frame perfect trick and just rerquires pratice. You know if you have succeeded as Kiki goes invisible but she is now in her "Small Mech" suit and will re-appear in the next screen.
Important note: Do not hammer the Y button, whist it increases your chance of pulling off the trick it can also result in you getting back in your mech again and negating a successful attempt.
Unfortunatley the game saves every time you attempt so it slowly eats your time but i recommend you start a new go, get to a save point and practice. I can get it after 4 or 5 attempts but at first it felt impossible so persevere. Skip to 1.24 in the video to see it's first instance.
You can save at a save point without losing Small Mech. You only lose it if you eject or reload a save.
Water MechMuch easier than Small Mech but still can be a pain. Basically you line your suit up with the very edge of a platform with the back side hanging over the edge. You then shoot a misslie with

to push yourself off the edge then immediately eject using the

button. Kiki jumps out, the suit sinks to the next availble floor. Swin to the suit and you pop straight in, voila, Water Mech.
I used like a sliding motion with my thumb, from the

to the

in a smooth quick motion and i could get it prettty often. I had more trouble lining the suit up with the edge than performing the trick itself.
Whilst in Water Mech missles immediatley explode, they dont travel at all. You can use this to boost yourself upward if you aim and shoot downward.
Again, the trick and then utilising the Water Mech efficiently come with practice. Skip to 4:09 in the video for the start of the explanation and first use of the trick.
I honestly spent the best part of 4 hours practising the tricks and the run. I would get to a save point, save and then return to title screen (as pausing in game does not pause the timer), find that point in the video, watch the next part until he came to a save point I could utilise and repeat that process.
Just practice, it's not the hardest thing in the world but it wont just happen. Good luck, any question ask below and i'll do my best to answer them.