Some tips that've helped me chain through the Omote mid-bosses: Stage 1 - predominate your laser on the small silos on the right hand side of the screen, flicking off the popcorns with your shot before the boss appears, hold your laser on the centre-right/right-hand side of the bosses form until it's last attack - making sure the small flotilla of popcorns is still just to your left - and when it's just about to blow flick your shot over them for a brief second and switch back to laser to kill the boss. You should have enough of a chain guage boost to carry your ship over to the far left and/or right to hit the remaning land based popcorns before the helicopters appear for the last past of the level.
Stage 2 - I've had some success keeping my eye mostly on the chain guage and tapping shot with a very slow but steady rhythm on the two swarms of Galaga type enemies that snake onto the screen, then obviously holding laser at the last one. For the destruction of the boss I've had success positioning my laser in the 2nd quarter of the screen (if you imagine the screen in quarters left to right - 1,2,3,4). Hypering through him is very easy this way (even possible to get some boost from his spawn) but make sure to start your finishing laser early as milking his early patterns for hits always tends to kill my chain easily.
Stage 3 - Not perfected this one but I get the impression positioning during the downwards-moving swarm and into the mini-midboss type thing plays a big part, with obviously the small popcorns at the bottom edge of the screen being crucial also. Can't say anything about holding the chain through it's death... don't think I've ever did it...
Stage 4 - I find chaining through the first Galaga type things into the chain of ships the hardest part - requires perfect memorization from what I can tell. The route up to the boss is actually quite simple with the path clearly laid out - make sure to grab up the popcorns that appear while your fighting the actual boss, can be hard to see them sometimes through it's pattern. I've found the destruction part to be hit or miss, but if you do catch the first helicopter, be sure to go easy on the little swarms that drop down by tapping shot slowly until your over land again and the first lasers appear.
As for Stage 5 - I find the Stage 5 Omote boss a nightmare in general (can no miss the Ura regularly without hypers...) so any tips on handling it's first pattern would be appreciated.