This app was mentioned in 8 comments, with an average of 1.75 upvotes
I haven't really run extensive tests, but Galaxy Hero is at least offline and completely free. Top-down scrolling shmup with an RPG levelup system (both in terms of killing enough enemies to get a stat increase with stats you increase manually, as well as weapons that evolve as they kill enemies). Kinda ugly, several graphics come from Tyrian (with permission), and it's perpetually unfinished though there's a long coliseum feature. Kinda a shame it's unfinished since the dev had some pretty cool ideas, but there's still a pretty good game left here. Just you start one sector and you get the "more coming soon!" message, so...
Anyway, this is one of those I leave on my devices. Levels are relatively short and there's no penalty for dying other than having to restart the level.
https://play.google.com/store/apps/details?id=com.galaxyhero.main - A top down space shooter/RPG hybrid. Lots of ship customization, a "Colosseum" mode where you're sent to some endless randomly generated waves called "Zones", and lots of stats to work on. Attack, Defense, Speed, Luck, Crit chance, and Specific Resistances.
Also yes, its easy on battery life...same as Soul Unleashed.
Galaxy Hero - https://play.google.com/store/apps/details?id=com.galaxyhero.main
Its basically a solid mix between an RPG and a shmup. It has loads of customization, it plays fair with any build by not rewarding based on skill (which also means it doesn't leave tank builds out in the dust), a Colosseum mode that acts like an endless space shooter with randomized waves, and just focuses on the action so there's not even a pretentious "The Earth is in danger" story to hold it back from the fun parts of this game.
It helps that its generous with battery consumption; I played it for relatively 25 minutes w/out headphones and only lost 5% charge on my 1700mah battery, which can't be said for most of my games.
It's ancient, it's ugly, and it's never going to be finished, but Galaxy Hero kind of fits the bill. You only get one type of ship but there are passive upgrades you can buy and different weapon types that you can level up, with "sidekick" ships to find/buy/unlock that also level up.
The different weapons have elements tied to them and enemies can be weak/strong versus specific ones, but just blasting away is effective too.
There's an endless mode where you face stronger and stronger enemies but I don't remember much about it other than it had a checkpoint system so you weren't starting at Zone 1 each time.
I have this game for over 4 years https://play.google.com/store/apps/details?id=com.galaxyhero.main
More of an RPG STG than an incremental, but it's the closest I've ever found: Galaxy Hero